# Applying derivatives to analyze functions

AP®︎ Calculus BC,

The first and the second derivative of a function can be used to obtain a lot of information about the behavior of that function. For example, the first derivative tells us where a function increases or decreases and where it has maximum or minimum points; the second derivative tells us where a function is concave up or down and where it has inflection points.

This course contains 13 segments:

Using the mean value theorem

Extreme value theorem, global versus local extrema, and critical points

Determining intervals on which a function is increasing or decreasing

Using the first derivative test to find relative (local) extrema

Using the candidates test to find absolute (global) extrema

Determining concavity of intervals and finding points of inflection: graphical

Determining concavity of intervals and finding points of inflection: algebraic

Using the second derivative test to find extrema

Sketching curves of functions and their derivatives

Connecting a function, its first derivative, and its second derivative

Solving optimization problems

Exploring behaviors of implicit relations

Calculator-active practice

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