Find the extrema using the second derivative test
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👉 Learn how to find the extrema of a function using the second derivative test. The second derivative test states that if a function has a critical point for which f'(x) = 0, and the second derivative is positive, then the function has a minimum point at that point. If the second derivative is negative, then the function has a maximum point at that point and if the second derivative is zero, then the function has an inflection point at that point.
To find the extrema of a function using the second derivative test, we first find the derivative of the function and equate it to zero. Then, we solve the resulting equation for x to get the critical points. Then take the second derivative of the function and substitute each of the critical points into the second derivative. The critical points for which the second derivative is positive represent minimum points, the critical points for which the second derivative is negative represent maximum points, while the critical points for which the second derivative is zero represent inflection points.
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Organized Videos:
✅Applications of the Derivative
Applications of the Derivative
✅Determine Increasing or Decreasing Function From a Table
Determine Increasing or Decreasing Fu...
✅Concavity of Functions
Concavity of Functions
✅Extreme Value Theorem of Functions
Extreme Value Theorem of Functions
✅First Derivative Test for Functions
First Derivative Test for Functions
✅Find the Critical Values of a Function
Find the Critical Values of a Function
✅Extrema, Concavity, Increasing Decreasing Intervals from a Graph
Extrema, Concavity, Increasing Decrea...
✅Sketch the Graph of the First and Second Derivative
Find the Points of Inflection of a Fu...
✅Find the Points of Inflection of a Function
Find the Points of Inflection of a Fu...
✅Second Derivative Test For a Function
Second Derivative Test For a Function
✅Intermediate Value Theorem of Functions
Intermediate Value Theorem of Functions
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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
To find the extrema of a function using the second derivative test, we first find the derivative of the function and equate it to zero. Then, we solve the resulting equation for x to get the critical points. Then take the second derivative of the function and substitute each of the critical points into the second derivative. The critical points for which the second derivative is positive represent minimum points, the critical points for which the second derivative is negative represent maximum points, while the critical points for which the second derivative is zero represent inflection points.
👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianm...
❤️Support my channel by becoming a member: @brianmclogan
🙋♂️Have questions? Ask here: https://forms.gle/dfR9HbCu6qpWbJdo7
🎉Follow the Community: mrbrianmclogan
Organized Videos:
✅Applications of the Derivative
Applications of the Derivative
✅Determine Increasing or Decreasing Function From a Table
Determine Increasing or Decreasing Fu...
✅Concavity of Functions
Concavity of Functions
✅Extreme Value Theorem of Functions
Extreme Value Theorem of Functions
✅First Derivative Test for Functions
First Derivative Test for Functions
✅Find the Critical Values of a Function
Find the Critical Values of a Function
✅Extrema, Concavity, Increasing Decreasing Intervals from a Graph
Extrema, Concavity, Increasing Decrea...
✅Sketch the Graph of the First and Second Derivative
Find the Points of Inflection of a Fu...
✅Find the Points of Inflection of a Function
Find the Points of Inflection of a Fu...
✅Second Derivative Test For a Function
Second Derivative Test For a Function
✅Intermediate Value Theorem of Functions
Intermediate Value Theorem of Functions
🗂️ Organized playlists by classes here: mrbrianmclogan
🌐 My Website - http://www.freemathvideos.com
🎯Survive Math Class Checklist: Ten Steps to a Better Year: https://www.brianmclogan.com/email-ca...
Connect with me:
⚡️Facebook - Facebook: freemathvideos
⚡️Instagram - Instagram: brianmclogan
⚡️Twitter - Twitter: mrbrianmclogan
⚡️Linkedin - LinkedIn: brian-mclogan-16b43623
👨🏫 Current Courses on Udemy: https://www.udemy.com/user/brianmclog...
👨👩👧👧 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
7 سال پیش
در تاریخ 1396/10/15 منتشر شده
است.
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