Analyzing functions

This course is a part of Differential Calculus, a 6-course Topic series from Khan Academy.

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:

Mean value theorem

Extreme value theorem and critical points

Intervals on which a function is increasing or decreasing

Relative (local) extrema

Absolute (global) extrema

Concavity and inflection points intro

Analyzing concavity and inflection points

Second derivative test

Sketching curves

Connecting f, f', and f''

Solving optimization problems

Analyzing implicit relations

Calculator-active practice