Second Derivative Test

This calculus video tutorial provides a basic introduction into the second derivative test. It explains how to use the second derivative test to identify the presence of a relative maximum or a relative minimum at a critical point. If the second derivative is positive at a critical number - a local minimum is present. If the second derivative is negative at a critical number - a local maximum is present. So to identify the relative extrema, find the first derivative, set it equal to zero and identify the critical numbers. Plug the critical numbers into the second derivative function to determine the concavity of the function to see if its concave up or concave down. If it's concave up - it's a relative maximum. If it's concave down, it's a relative minimum. You can confirm the results of the second derivative test using the first derivative test with a sign chart on a number line.

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

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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

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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

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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

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https://www.video-tutor.net/

Full-Length Videos and Worksheets:
https://www.patreon.com/MathSc....ienceTutor/collectio