In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap or upper convex.
Definition
A real-valued functionf on an interval (or, more generally, a convex set in vector space) is said to be concave if, for any x and y in the interval and for any t in [0,1],
A function is called strictly concave if
for any t in (0,1) and x ≠ y.
For a function f:R→R, this definition merely states that for every z between x and y, the point (z, f(z) ) on the graph of f is above the straight line joining the points (x, f(x) ) and (y, f(y) ).
A function f is quasiconcave if the upper contour sets of the function are convex sets.
In this video I break down the formal definition of a concave function and attempt to explain all aspects and variables used in the definition. Being that a convex function is just the opposite in terms of its definition, once one of them is well understood the other is also understood.
If anyone has any questions or is still unsure on any concepts covered in the vid put them in the comment section and il try my best to answer.
published: 18 Oct 2020
Concavity, Inflection Points, and Second Derivative
This calculus video tutorial provides a basic introduction into concavity and inflection points. It explains how to find the inflections point of a function using the second derivative and how to find the intervals where the function is concave up and concave down using a sign chart on a number line. When the second derivative is positive, the function is concave up which means the first derivative is increasing. When the second derivative is negative, the function is concave down which indicates that the first derivative is decreasing.
Derivative Applications - Free Formula Sheet:
https://bit.ly/4eV6r1b
Calculus 1 Final Exam Review:
https://www.youtube.com/watch?v=WmBzmHru78w
____________________________
Introduction to Limits:
https://www.youtu...
published: 04 Mar 2018
Concavity, Inflection Points, Increasing Decreasing, First & Second Derivative - Calculus
This calculus video tutorial shows you how to find the intervals where the function is increasing and decreasing, the critical points or critical numbers, relative extrema such as local minimum and local maximum values using the first derivative test, concavity, and inflection points using the second derivative.
Derivative Applications - Free Formula Sheet:
https://bit.ly/4eV6r1b
Calculus 1 Final Exam Review:
https://www.youtube.com/watch?v=WmBzmHru78w
Derivative Applications - Video Lessons:
https://www.video-tutor.net/derivative-applications.html
published: 29 Sep 2016
Convex and Concave Functions
For the book, you may refer: https://amzn.to/3aT4ino
This lecture explains how to check whether the function is convex or concave.
Other lectures:
Quadratic form: https://youtu.be/6jjTLDX_JOk
Hessian Matrix: https://youtu.be/mJB-XLV0QJc
Convex & Concave function: https://youtu.be/nZ7vjo2dQ1o
Maxima & Minima of the function: https://youtu.be/gJHgIcMeS2M
published: 01 Apr 2021
Concave and convex functions
http://www.learnitt.com/. For Assignment Help/Homework Help in Economics, Mathematics and Statistics please visit http://www.learnitt.com/. This video explains what are concave functions and convex functions
published: 14 Aug 2012
Learn how to determine concavity and point of inflection AP style
👉 Learn how to determine the concavity of a function. A function is said to be concave up (convex) if the graph of the curve is facing upwards and the function is said to be concave down (concave) if the graph is facing down.
To test for the concavity of a function, we find the second derivatives of the function. Given a function y = f(x), the graph is concave up (convex) in the intervals where the second derivative of the function is positive. The graph is concave down (concave) in the intervals where the second derivative of the function is negative. And the graph has a point of inflection at the points where the second derivative of the function is zero.
👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1
❤️Support my channel by becoming a m...
published: 28 Dec 2016
Concavity introduction | Using derivatives to analyze functions | AP Calculus AB | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-6a/v/concavity-concave-upwards-and-concave-downwards-intervals
Sal introduces the concept of concavity, what it means for a graph to be "concave up" or "concave down," and how this relates to the second derivative of a function. Created by Sal Khan.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-concavity/e/recognizing_concavity?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-concavity/v/recognizin...
published: 31 Jan 2013
Lecture 15: Concave up and Concave down of a function using examples.
published: 07 Jul 2021
Concave And Convex Function SHORTCUT | Function Of One Variable - Real Analysis By GP Sir
Comment Your Answer, And Faida Hua Toh Share Kariye
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published: 09 Aug 2021
What is concavity of a graph
👉 Learn how to determine the concavity of a function. A function is said to be concave up (convex) if the graph of the curve is facing upwards and the function is said to be concave down (concave) if the graph is facing down.
To test for the concavity of a function, we find the second derivatives of the function. Given a function y = f(x), the graph is concave up (convex) in the intervals where the second derivative of the function is positive. The graph is concave down (concave) in the intervals where the second derivative of the function is negative. And the graph has a point of inflection at the points where the second derivative of the function is zero.
👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1
❤️Support my channel by becoming a m...
In this video I break down the formal definition of a concave function and attempt to explain all aspects and variables used in the definition. Being that a con...
In this video I break down the formal definition of a concave function and attempt to explain all aspects and variables used in the definition. Being that a convex function is just the opposite in terms of its definition, once one of them is well understood the other is also understood.
If anyone has any questions or is still unsure on any concepts covered in the vid put them in the comment section and il try my best to answer.
In this video I break down the formal definition of a concave function and attempt to explain all aspects and variables used in the definition. Being that a convex function is just the opposite in terms of its definition, once one of them is well understood the other is also understood.
If anyone has any questions or is still unsure on any concepts covered in the vid put them in the comment section and il try my best to answer.
This calculus video tutorial provides a basic introduction into concavity and inflection points. It explains how to find the inflections point of a function us...
This calculus video tutorial provides a basic introduction into concavity and inflection points. It explains how to find the inflections point of a function using the second derivative and how to find the intervals where the function is concave up and concave down using a sign chart on a number line. When the second derivative is positive, the function is concave up which means the first derivative is increasing. When the second derivative is negative, the function is concave down which indicates that the first derivative is decreasing.
Derivative Applications - Free Formula Sheet:
https://bit.ly/4eV6r1b
Calculus 1 Final Exam Review:
https://www.youtube.com/watch?v=WmBzmHru78w
____________________________
Introduction to Limits:
https://www.youtube.com/watch?v=YNstP0ESndU
Derivatives - Fast Review:
https://www.youtube.com/watch?v=5yfh5cf4-0w
Introduction to Related Rates:
https://www.youtube.com/watch?v=I9mVUo-bhM8
_____________________________
Extreme Value Theorem:
https://www.youtube.com/watch?v=Sx2lPZlnWfs
Finding Critical Numbers:
https://www.youtube.com/watch?v=Bp9EbV3COVA
Local Maximum & Minimum:
https://www.youtube.com/watch?v=WCq3sRzsJfs
Absolute Extrema:
https://www.youtube.com/watch?v=3wrXDw5ETh4
Rolle's Theorem:
https://www.youtube.com/watch?v=LHym1ARc2cE
________________________________
Mean Value Theorem:
https://www.youtube.com/watch?v=SL2RobwU_M4
Increasing and Decreasing Functions:
https://www.youtube.com/watch?v=Dyl7jPlJXOM
First Derivative Test:
https://www.youtube.com/watch?v=G5wlKltW7pM
Concavity & Inflection Points:
https://www.youtube.com/watch?v=OhqNbQi9QPk
Second Derivative Test:
https://www.youtube.com/watch?v=G8GAsYkZlpE
_________________________________
L'Hopital's Rule:
https://www.youtube.com/watch?v=Gh48aOvWcxw
Curve Sketching with Derivatives:
https://www.youtube.com/watch?v=JTVNUdL7sWs
Newton's Method:
https://www.youtube.com/watch?v=-5e2cULI3H8
Optimization Problems:
https://www.youtube.com/watch?v=lx8RcYcYVuU
_______________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
This calculus video tutorial provides a basic introduction into concavity and inflection points. It explains how to find the inflections point of a function using the second derivative and how to find the intervals where the function is concave up and concave down using a sign chart on a number line. When the second derivative is positive, the function is concave up which means the first derivative is increasing. When the second derivative is negative, the function is concave down which indicates that the first derivative is decreasing.
Derivative Applications - Free Formula Sheet:
https://bit.ly/4eV6r1b
Calculus 1 Final Exam Review:
https://www.youtube.com/watch?v=WmBzmHru78w
____________________________
Introduction to Limits:
https://www.youtube.com/watch?v=YNstP0ESndU
Derivatives - Fast Review:
https://www.youtube.com/watch?v=5yfh5cf4-0w
Introduction to Related Rates:
https://www.youtube.com/watch?v=I9mVUo-bhM8
_____________________________
Extreme Value Theorem:
https://www.youtube.com/watch?v=Sx2lPZlnWfs
Finding Critical Numbers:
https://www.youtube.com/watch?v=Bp9EbV3COVA
Local Maximum & Minimum:
https://www.youtube.com/watch?v=WCq3sRzsJfs
Absolute Extrema:
https://www.youtube.com/watch?v=3wrXDw5ETh4
Rolle's Theorem:
https://www.youtube.com/watch?v=LHym1ARc2cE
________________________________
Mean Value Theorem:
https://www.youtube.com/watch?v=SL2RobwU_M4
Increasing and Decreasing Functions:
https://www.youtube.com/watch?v=Dyl7jPlJXOM
First Derivative Test:
https://www.youtube.com/watch?v=G5wlKltW7pM
Concavity & Inflection Points:
https://www.youtube.com/watch?v=OhqNbQi9QPk
Second Derivative Test:
https://www.youtube.com/watch?v=G8GAsYkZlpE
_________________________________
L'Hopital's Rule:
https://www.youtube.com/watch?v=Gh48aOvWcxw
Curve Sketching with Derivatives:
https://www.youtube.com/watch?v=JTVNUdL7sWs
Newton's Method:
https://www.youtube.com/watch?v=-5e2cULI3H8
Optimization Problems:
https://www.youtube.com/watch?v=lx8RcYcYVuU
_______________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
This calculus video tutorial shows you how to find the intervals where the function is increasing and decreasing, the critical points or critical numbers, relat...
This calculus video tutorial shows you how to find the intervals where the function is increasing and decreasing, the critical points or critical numbers, relative extrema such as local minimum and local maximum values using the first derivative test, concavity, and inflection points using the second derivative.
Derivative Applications - Free Formula Sheet:
https://bit.ly/4eV6r1b
Calculus 1 Final Exam Review:
https://www.youtube.com/watch?v=WmBzmHru78w
Derivative Applications - Video Lessons:
https://www.video-tutor.net/derivative-applications.html
This calculus video tutorial shows you how to find the intervals where the function is increasing and decreasing, the critical points or critical numbers, relative extrema such as local minimum and local maximum values using the first derivative test, concavity, and inflection points using the second derivative.
Derivative Applications - Free Formula Sheet:
https://bit.ly/4eV6r1b
Calculus 1 Final Exam Review:
https://www.youtube.com/watch?v=WmBzmHru78w
Derivative Applications - Video Lessons:
https://www.video-tutor.net/derivative-applications.html
For the book, you may refer: https://amzn.to/3aT4ino
This lecture explains how to check whether the function is convex or concave.
Other lectures:
Quadratic f...
For the book, you may refer: https://amzn.to/3aT4ino
This lecture explains how to check whether the function is convex or concave.
Other lectures:
Quadratic form: https://youtu.be/6jjTLDX_JOk
Hessian Matrix: https://youtu.be/mJB-XLV0QJc
Convex & Concave function: https://youtu.be/nZ7vjo2dQ1o
Maxima & Minima of the function: https://youtu.be/gJHgIcMeS2M
For the book, you may refer: https://amzn.to/3aT4ino
This lecture explains how to check whether the function is convex or concave.
Other lectures:
Quadratic form: https://youtu.be/6jjTLDX_JOk
Hessian Matrix: https://youtu.be/mJB-XLV0QJc
Convex & Concave function: https://youtu.be/nZ7vjo2dQ1o
Maxima & Minima of the function: https://youtu.be/gJHgIcMeS2M
http://www.learnitt.com/. For Assignment Help/Homework Help in Economics, Mathematics and Statistics please visit http://www.learnitt.com/. This video explains ...
http://www.learnitt.com/. For Assignment Help/Homework Help in Economics, Mathematics and Statistics please visit http://www.learnitt.com/. This video explains what are concave functions and convex functions
http://www.learnitt.com/. For Assignment Help/Homework Help in Economics, Mathematics and Statistics please visit http://www.learnitt.com/. This video explains what are concave functions and convex functions
👉 Learn how to determine the concavity of a function. A function is said to be concave up (convex) if the graph of the curve is facing upwards and the function ...
👉 Learn how to determine the concavity of a function. A function is said to be concave up (convex) if the graph of the curve is facing upwards and the function is said to be concave down (concave) if the graph is facing down.
To test for the concavity of a function, we find the second derivatives of the function. Given a function y = f(x), the graph is concave up (convex) in the intervals where the second derivative of the function is positive. The graph is concave down (concave) in the intervals where the second derivative of the function is negative. And the graph has a point of inflection at the points where the second derivative of the function is zero.
👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1
❤️Support my channel by becoming a member: https://www.youtube.com/channel/UCQv3dpUXUWvDFQarHrS5P9A/join
🙋♂️Have questions? Ask here: https://forms.gle/dfR9HbCu6qpWbJdo7
🎉Follow the Community: https://www.youtube.com/user/MrBrianMcLogan/community
Organized Videos:
✅Applications of the Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrcSuJvgrXcmzJtTCnRonNf
✅Determine Increasing or Decreasing Function From a Table
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMr9j-FdiaerwTUCNPbq60YU
✅Concavity of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpimVpMRNk9RoMqU1Bnc3QX
✅Extreme Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqZb_T6ISeUVqck6A9q47C9
✅First Derivative Test for Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrrDgvZOhP7cNPKA-x7CFji
✅Find the Critical Values of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrIH6aTbIadngG-1VdBP6mU
✅Extrema, Concavity, Increasing Decreasing Intervals from a Graph
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqfmQ6mK3Aa9ZqaxU1l7AtM
✅Sketch the Graph of the First and Second Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Find the Points of Inflection of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Second Derivative Test For a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqvfbGFMscX_3JoYmanH-6a
✅Intermediate Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpC61uxuKi7KlgsE0y-48bR
🗂️ Organized playlists by classes here: https://www.youtube.com/user/MrBrianMcLogan/playlists
🌐 My Website - http://www.freemathvideos.com
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👨🏫 Current Courses on Udemy: https://www.udemy.com/user/brianmclogan2/
👨👩👧👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: https://www.freemathvideos.com/about-me/
#derivatives #brianmclogan
👉 Learn how to determine the concavity of a function. A function is said to be concave up (convex) if the graph of the curve is facing upwards and the function is said to be concave down (concave) if the graph is facing down.
To test for the concavity of a function, we find the second derivatives of the function. Given a function y = f(x), the graph is concave up (convex) in the intervals where the second derivative of the function is positive. The graph is concave down (concave) in the intervals where the second derivative of the function is negative. And the graph has a point of inflection at the points where the second derivative of the function is zero.
👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1
❤️Support my channel by becoming a member: https://www.youtube.com/channel/UCQv3dpUXUWvDFQarHrS5P9A/join
🙋♂️Have questions? Ask here: https://forms.gle/dfR9HbCu6qpWbJdo7
🎉Follow the Community: https://www.youtube.com/user/MrBrianMcLogan/community
Organized Videos:
✅Applications of the Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrcSuJvgrXcmzJtTCnRonNf
✅Determine Increasing or Decreasing Function From a Table
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMr9j-FdiaerwTUCNPbq60YU
✅Concavity of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpimVpMRNk9RoMqU1Bnc3QX
✅Extreme Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqZb_T6ISeUVqck6A9q47C9
✅First Derivative Test for Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrrDgvZOhP7cNPKA-x7CFji
✅Find the Critical Values of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrIH6aTbIadngG-1VdBP6mU
✅Extrema, Concavity, Increasing Decreasing Intervals from a Graph
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqfmQ6mK3Aa9ZqaxU1l7AtM
✅Sketch the Graph of the First and Second Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Find the Points of Inflection of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Second Derivative Test For a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqvfbGFMscX_3JoYmanH-6a
✅Intermediate Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpC61uxuKi7KlgsE0y-48bR
🗂️ Organized playlists by classes here: https://www.youtube.com/user/MrBrianMcLogan/playlists
🌐 My Website - http://www.freemathvideos.com
🎯Survive Math Class Checklist: Ten Steps to a Better Year: https://www.brianmclogan.com/email-capture-fdea604e-9ee8-433f-aa93-c6fefdfe4d57
Connect with me:
⚡️Facebook - https://www.facebook.com/freemathvideos
⚡️Instagram - https://www.instagram.com/brianmclogan/
⚡️Twitter - https://twitter.com/mrbrianmclogan
⚡️Linkedin - https://www.linkedin.com/in/brian-mclogan-16b43623/
👨🏫 Current Courses on Udemy: https://www.udemy.com/user/brianmclogan2/
👨👩👧👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: https://www.freemathvideos.com/about-me/
#derivatives #brianmclogan
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical...
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-6a/v/concavity-concave-upwards-and-concave-downwards-intervals
Sal introduces the concept of concavity, what it means for a graph to be "concave up" or "concave down," and how this relates to the second derivative of a function. Created by Sal Khan.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-concavity/e/recognizing_concavity?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-concavity/v/recognizing-concavity-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-find-abs-extrema/v/absolute-extrema-on-entire-domain?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-6a/v/concavity-concave-upwards-and-concave-downwards-intervals
Sal introduces the concept of concavity, what it means for a graph to be "concave up" or "concave down," and how this relates to the second derivative of a function. Created by Sal Khan.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-concavity/e/recognizing_concavity?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-concavity/v/recognizing-concavity-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-find-abs-extrema/v/absolute-extrema-on-entire-domain?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
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Short Cuts & Tricks -
{Solve Determinants i...
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Short Cuts & Tricks -
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{Inverse & Adj(A) of 3x3 & 2x2 Matrix} - https://youtu.be/31RhJeGoTmM
{Characteristic Polynomial 3x3 & 2x2} - https://youtu.be/QfF_whXs_CA
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Concave And Convex Function SHORTCUT | Function Of One Variable - Real Analysis By GP Sir - Short Trick By GP Sir | By @Dr.Gajendra Purohit - GP Sir
Time Stamp
0:00 - Trick with example of Concave and convex function
2:40 - Q1. Based on Concave and convex
3:14 - Q2. Based on Concave and convex
3:45 - Q1. answer asked in Comment box based on Concave and convex
4:04 - Detailed about old videos
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{Characteristic Polynomial 3x3 & 2x2} - https://youtu.be/QfF_whXs_CA
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------------------------------------------------
Concave And Convex Function SHORTCUT | Function Of One Variable - Real Analysis By GP Sir - Short Trick By GP Sir | By @Dr.Gajendra Purohit - GP Sir
Time Stamp
0:00 - Trick with example of Concave and convex function
2:40 - Q1. Based on Concave and convex
3:14 - Q2. Based on Concave and convex
3:45 - Q1. answer asked in Comment box based on Concave and convex
4:04 - Detailed about old videos
-----------------------------------------------
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📚 Following Topics Are Also Available
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▶️Complex Analysis: https://bit.ly/3vnBk8D
▶️Differential Equation: https://bit.ly/38FnAMH
▶️Partial Differentiation: https://bit.ly/3tkNaOV
▶️Numerical Analysis: https://bit.ly/3vrlEkA
▶️Operation Research: https://bit.ly/3cvBxOq
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▶️Integral Calculus: https://bit.ly/3qIOtFz
▶️Differential Calculus: https://bit.ly/3bM9CKT
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👉 Learn how to determine the concavity of a function. A function is said to be concave up (convex) if the graph of the curve is facing upwards and the function ...
👉 Learn how to determine the concavity of a function. A function is said to be concave up (convex) if the graph of the curve is facing upwards and the function is said to be concave down (concave) if the graph is facing down.
To test for the concavity of a function, we find the second derivatives of the function. Given a function y = f(x), the graph is concave up (convex) in the intervals where the second derivative of the function is positive. The graph is concave down (concave) in the intervals where the second derivative of the function is negative. And the graph has a point of inflection at the points where the second derivative of the function is zero.
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Organized Videos:
✅Applications of the Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrcSuJvgrXcmzJtTCnRonNf
✅Determine Increasing or Decreasing Function From a Table
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMr9j-FdiaerwTUCNPbq60YU
✅Concavity of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpimVpMRNk9RoMqU1Bnc3QX
✅Extreme Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqZb_T6ISeUVqck6A9q47C9
✅First Derivative Test for Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrrDgvZOhP7cNPKA-x7CFji
✅Find the Critical Values of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrIH6aTbIadngG-1VdBP6mU
✅Extrema, Concavity, Increasing Decreasing Intervals from a Graph
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqfmQ6mK3Aa9ZqaxU1l7AtM
✅Sketch the Graph of the First and Second Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Find the Points of Inflection of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Second Derivative Test For a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqvfbGFMscX_3JoYmanH-6a
✅Intermediate Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpC61uxuKi7KlgsE0y-48bR
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#derivatives #brianmclogan
👉 Learn how to determine the concavity of a function. A function is said to be concave up (convex) if the graph of the curve is facing upwards and the function is said to be concave down (concave) if the graph is facing down.
To test for the concavity of a function, we find the second derivatives of the function. Given a function y = f(x), the graph is concave up (convex) in the intervals where the second derivative of the function is positive. The graph is concave down (concave) in the intervals where the second derivative of the function is negative. And the graph has a point of inflection at the points where the second derivative of the function is zero.
👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1
❤️Support my channel by becoming a member: https://www.youtube.com/channel/UCQv3dpUXUWvDFQarHrS5P9A/join
🙋♂️Have questions? Ask here: https://forms.gle/dfR9HbCu6qpWbJdo7
🎉Follow the Community: https://www.youtube.com/user/MrBrianMcLogan/community
Organized Videos:
✅Applications of the Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrcSuJvgrXcmzJtTCnRonNf
✅Determine Increasing or Decreasing Function From a Table
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMr9j-FdiaerwTUCNPbq60YU
✅Concavity of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpimVpMRNk9RoMqU1Bnc3QX
✅Extreme Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqZb_T6ISeUVqck6A9q47C9
✅First Derivative Test for Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrrDgvZOhP7cNPKA-x7CFji
✅Find the Critical Values of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrIH6aTbIadngG-1VdBP6mU
✅Extrema, Concavity, Increasing Decreasing Intervals from a Graph
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqfmQ6mK3Aa9ZqaxU1l7AtM
✅Sketch the Graph of the First and Second Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Find the Points of Inflection of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Second Derivative Test For a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqvfbGFMscX_3JoYmanH-6a
✅Intermediate Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpC61uxuKi7KlgsE0y-48bR
🗂️ Organized playlists by classes here: https://www.youtube.com/user/MrBrianMcLogan/playlists
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👨👩👧👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: https://www.freemathvideos.com/about-me/
#derivatives #brianmclogan
In this video I break down the formal definition of a concave function and attempt to explain all aspects and variables used in the definition. Being that a convex function is just the opposite in terms of its definition, once one of them is well understood the other is also understood.
If anyone has any questions or is still unsure on any concepts covered in the vid put them in the comment section and il try my best to answer.
This calculus video tutorial provides a basic introduction into concavity and inflection points. It explains how to find the inflections point of a function using the second derivative and how to find the intervals where the function is concave up and concave down using a sign chart on a number line. When the second derivative is positive, the function is concave up which means the first derivative is increasing. When the second derivative is negative, the function is concave down which indicates that the first derivative is decreasing.
Derivative Applications - Free Formula Sheet:
https://bit.ly/4eV6r1b
Calculus 1 Final Exam Review:
https://www.youtube.com/watch?v=WmBzmHru78w
____________________________
Introduction to Limits:
https://www.youtube.com/watch?v=YNstP0ESndU
Derivatives - Fast Review:
https://www.youtube.com/watch?v=5yfh5cf4-0w
Introduction to Related Rates:
https://www.youtube.com/watch?v=I9mVUo-bhM8
_____________________________
Extreme Value Theorem:
https://www.youtube.com/watch?v=Sx2lPZlnWfs
Finding Critical Numbers:
https://www.youtube.com/watch?v=Bp9EbV3COVA
Local Maximum & Minimum:
https://www.youtube.com/watch?v=WCq3sRzsJfs
Absolute Extrema:
https://www.youtube.com/watch?v=3wrXDw5ETh4
Rolle's Theorem:
https://www.youtube.com/watch?v=LHym1ARc2cE
________________________________
Mean Value Theorem:
https://www.youtube.com/watch?v=SL2RobwU_M4
Increasing and Decreasing Functions:
https://www.youtube.com/watch?v=Dyl7jPlJXOM
First Derivative Test:
https://www.youtube.com/watch?v=G5wlKltW7pM
Concavity & Inflection Points:
https://www.youtube.com/watch?v=OhqNbQi9QPk
Second Derivative Test:
https://www.youtube.com/watch?v=G8GAsYkZlpE
_________________________________
L'Hopital's Rule:
https://www.youtube.com/watch?v=Gh48aOvWcxw
Curve Sketching with Derivatives:
https://www.youtube.com/watch?v=JTVNUdL7sWs
Newton's Method:
https://www.youtube.com/watch?v=-5e2cULI3H8
Optimization Problems:
https://www.youtube.com/watch?v=lx8RcYcYVuU
_______________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
This calculus video tutorial shows you how to find the intervals where the function is increasing and decreasing, the critical points or critical numbers, relative extrema such as local minimum and local maximum values using the first derivative test, concavity, and inflection points using the second derivative.
Derivative Applications - Free Formula Sheet:
https://bit.ly/4eV6r1b
Calculus 1 Final Exam Review:
https://www.youtube.com/watch?v=WmBzmHru78w
Derivative Applications - Video Lessons:
https://www.video-tutor.net/derivative-applications.html
For the book, you may refer: https://amzn.to/3aT4ino
This lecture explains how to check whether the function is convex or concave.
Other lectures:
Quadratic form: https://youtu.be/6jjTLDX_JOk
Hessian Matrix: https://youtu.be/mJB-XLV0QJc
Convex & Concave function: https://youtu.be/nZ7vjo2dQ1o
Maxima & Minima of the function: https://youtu.be/gJHgIcMeS2M
http://www.learnitt.com/. For Assignment Help/Homework Help in Economics, Mathematics and Statistics please visit http://www.learnitt.com/. This video explains what are concave functions and convex functions
👉 Learn how to determine the concavity of a function. A function is said to be concave up (convex) if the graph of the curve is facing upwards and the function is said to be concave down (concave) if the graph is facing down.
To test for the concavity of a function, we find the second derivatives of the function. Given a function y = f(x), the graph is concave up (convex) in the intervals where the second derivative of the function is positive. The graph is concave down (concave) in the intervals where the second derivative of the function is negative. And the graph has a point of inflection at the points where the second derivative of the function is zero.
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Organized Videos:
✅Applications of the Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrcSuJvgrXcmzJtTCnRonNf
✅Determine Increasing or Decreasing Function From a Table
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMr9j-FdiaerwTUCNPbq60YU
✅Concavity of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpimVpMRNk9RoMqU1Bnc3QX
✅Extreme Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqZb_T6ISeUVqck6A9q47C9
✅First Derivative Test for Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrrDgvZOhP7cNPKA-x7CFji
✅Find the Critical Values of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrIH6aTbIadngG-1VdBP6mU
✅Extrema, Concavity, Increasing Decreasing Intervals from a Graph
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqfmQ6mK3Aa9ZqaxU1l7AtM
✅Sketch the Graph of the First and Second Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Find the Points of Inflection of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Second Derivative Test For a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqvfbGFMscX_3JoYmanH-6a
✅Intermediate Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpC61uxuKi7KlgsE0y-48bR
🗂️ Organized playlists by classes here: https://www.youtube.com/user/MrBrianMcLogan/playlists
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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-6a/v/concavity-concave-upwards-and-concave-downwards-intervals
Sal introduces the concept of concavity, what it means for a graph to be "concave up" or "concave down," and how this relates to the second derivative of a function. Created by Sal Khan.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-concavity/e/recognizing_concavity?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-concavity/v/recognizing-concavity-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-derivatives-analyze-functions/ab-find-abs-extrema/v/absolute-extrema-on-entire-domain?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
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Concave And Convex Function SHORTCUT | Function Of One Variable - Real Analysis By GP Sir - Short Trick By GP Sir | By @Dr.Gajendra Purohit - GP Sir
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0:00 - Trick with example of Concave and convex function
2:40 - Q1. Based on Concave and convex
3:14 - Q2. Based on Concave and convex
3:45 - Q1. answer asked in Comment box based on Concave and convex
4:04 - Detailed about old videos
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👉 Learn how to determine the concavity of a function. A function is said to be concave up (convex) if the graph of the curve is facing upwards and the function is said to be concave down (concave) if the graph is facing down.
To test for the concavity of a function, we find the second derivatives of the function. Given a function y = f(x), the graph is concave up (convex) in the intervals where the second derivative of the function is positive. The graph is concave down (concave) in the intervals where the second derivative of the function is negative. And the graph has a point of inflection at the points where the second derivative of the function is zero.
👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1
❤️Support my channel by becoming a member: https://www.youtube.com/channel/UCQv3dpUXUWvDFQarHrS5P9A/join
🙋♂️Have questions? Ask here: https://forms.gle/dfR9HbCu6qpWbJdo7
🎉Follow the Community: https://www.youtube.com/user/MrBrianMcLogan/community
Organized Videos:
✅Applications of the Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrcSuJvgrXcmzJtTCnRonNf
✅Determine Increasing or Decreasing Function From a Table
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMr9j-FdiaerwTUCNPbq60YU
✅Concavity of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpimVpMRNk9RoMqU1Bnc3QX
✅Extreme Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqZb_T6ISeUVqck6A9q47C9
✅First Derivative Test for Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrrDgvZOhP7cNPKA-x7CFji
✅Find the Critical Values of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrIH6aTbIadngG-1VdBP6mU
✅Extrema, Concavity, Increasing Decreasing Intervals from a Graph
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqfmQ6mK3Aa9ZqaxU1l7AtM
✅Sketch the Graph of the First and Second Derivative
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Find the Points of Inflection of a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMphsk2sW7h6zCmoY-VF1ID3
✅Second Derivative Test For a Function
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqvfbGFMscX_3JoYmanH-6a
✅Intermediate Value Theorem of Functions
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpC61uxuKi7KlgsE0y-48bR
🗂️ Organized playlists by classes here: https://www.youtube.com/user/MrBrianMcLogan/playlists
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👨👩👧👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: https://www.freemathvideos.com/about-me/
#derivatives #brianmclogan
In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap or upper convex.
Definition
A real-valued functionf on an interval (or, more generally, a convex set in vector space) is said to be concave if, for any x and y in the interval and for any t in [0,1],
A function is called strictly concave if
for any t in (0,1) and x ≠ y.
For a function f:R→R, this definition merely states that for every z between x and y, the point (z, f(z) ) on the graph of f is above the straight line joining the points (x, f(x) ) and (y, f(y) ).
A function f is quasiconcave if the upper contour sets of the function are convex sets.
The touch screen button on the top of W-Cat is placed on the side, using physical buttons and featuring a child lock function for added protection against accidental cat contact.
Measuring approximately 3 inches in diameter and 3mm thick, this round concave glass mirror is designed with educational use in mind, which may result in minor imperfections that do not impact its functionality.
The sculptural stool is highly versatile in function and form, serving as side table and objet d'art. The concave top and bottom of each stool is designed so that it can be placed either way up—a ...
This summer, the polar bears living at Beijing Zoo have two icy beds. The outdoor bed is concave and functions roughly like a household refrigerator ... The polar bears also have a chessboard-style shade over their swimming pool ... (Web editor ... .
This summer, the polar bears living at Beijing Zoo have two icy beds. The outdoor bed is concave and functions roughly like a household refrigerator ... The polar bears also have a chessboard-style shade over their swimming pool ... ....
PSVR 2 specs. Resolution. 2,000 x 2,040 per panel. Refresh rate. Up to 120Hz. Display ... Both the power button and camera function are located on the underside of the headset, and thus can be a little fiddly to press, especially as they’re slightly concave.
At the rear, the car comes fitted with the same quad tail-lights as the X Speedium Coupe and the X Concept, whereas the tailgate is inspired by the wings and crest of the Genesis logo.Cooling of the ...
The concave body recesses and splitter with aerodynamic sideblades also reflect design, as well as functional themes of the front end ... This functional feature ensures driving stability and reduces turbulence behind the vehicle and thus drag.
For example, one demonstrated device functions both as a converging lens that focuses light at one color, and as a concave lens that disperses light at a second color, while staying transparent, like ...