Applying Second Derivative Test for Extrema | Relative Extrema Determination Guide

Dec 26, 2024

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Learn how to utilize the Second Derivative Test to identify relative extrema in functions. Understand when the second derivative is positive for a relative minimum, negative for a relative maximum, or inconclusive. Practice problems included.

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Applying Second Derivative Test for Extrema | Relative Extrema Determination Guide

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3.4: Concavity and the Second Derivative Test
Objectives • Apply the Second Derivative Test to find relative extrema of a function.
2nd Derivative Test Find all the critical points, c • If f ''(c) > 0, f(c) is a relative minimum. • If f ''(c) < 0, f(c) is a relative maximum. • If f ''(c) = 0, the test is inconclusive. (Use the 1st derivative test.)