Concavity, Inflection Points, and The Second Derivative

Definition

Concavity refers to the shape of a graph and whether it is curving upward (concave up) or downward (concave down). Inflection points are locations on a graph where the concavity changes. The second derivative is used to determine the concavity of a function.

Related terms

First and Second Derivative Tests for Local Extrema:

These tests focus on identifying local extrema within an interval rather than considering all possible intervals.

Candidates Test for Global Extrema:

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

Critical Points:

These are values in the domain of a function where either its derivative is zero or undefined. They can indicate potential extrema or inflection points.