The Second Derivative Test for Relative Maximum and Minimum - Concept

Concept Concept (1)

The second derivative test is useful when trying to find a relative maximum or minimum if a function has a first derivative that is zero at a certain point. Since the first derivative test fails at this point, the point is an inflection point. The second derivative test relies on the sign of the second derivative at that point. If it is positive, the point is a relative minimum, and if it is negative, the point is a relative maximum.

Sample Sample Problems (3)

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The Second Derivative Test for Relative Maximum and Minimum - Problem 1
Problem 1
How to find the relative maxima and minima of a fourth degree polynomial function with three terms, using the second derivative test.
The Second Derivative Test for Relative Maximum and Minimum - Problem 2
Problem 2
How to find the relative maxima and minima of a product of functions, using the second derivative test.
The Second Derivative Test for Relative Maximum and Minimum - Problem 3
Problem 3
How to use the second derivative test to find the relative maxima and minima of a fourth degree polynomial function with five terms.