## Features Of the Derivative Graph

Any function can be graph. When a function is differentiated, aderivative function is the result. This derivative function can begraphed, and features of the derivative graph may tell us somethingabout the original graph. In particular, we can identify stationarypoints and determine their nature.

Suppose a function hasderivative thegraph of which is sketched below. At the point A, sothe point A is a stationary point for Since thepoint A is a maximum.

At the point B, sothe point B is a point of inflection for Since the point B is a non stationary point of inflection.

At the point C, sothe point C is a stationary point for Since the point C is a minimum.

The graph below has three points of inflexion. At the point A, so the point A is a point of inflexion for Since thepoint A is a non stationary point of inflexion.

At the point B, sothe point B is a point of inflection for Since the point B is a stationary point of inflection.

At the point C, sothe point C is a point of inflexion for Since thepoint A is a non stationary point of inflexion.