First and Second Derivative Tests for Local Extrema

Definition

The first and second derivative tests are methods used to determine the presence of local extrema (maximum or minimum points) on a function. The first derivative test involves analyzing the sign changes of the first derivative around critical points, while the second derivative test examines the concavity of the function at those points.

Related terms

Candidates Test for Global Extrema:

This method involves evaluating the function at its endpoints and critical points to find potential global extrema.

Concavity:

It refers to whether a graph is curving upward (concave up) or downward (concave down).

Inflection Points:

These are points where the concavity of a graph changes, indicating possible changes in curvature.