### Home > CALC > Chapter 5 > Lesson 5.2.4 > Problem 5-98

5-98.

Using the graph of

*f*′(*x*), determine the values of*x*where*f*(*x*) has a local minimum, local maximum or point of inflection. Justify your answer for each point. Homework Help ✎

You are looking at a graph of *f* '(*x*), which shows all the slopes of *f*(*x*).

A local minimum on *f*(*x*) is located where the slopes of *f*(*x*) change from negative to positive.

A local maximum on *f*(*x*) is located where the slopes of *f*(*x*) change from positive to negative.

An inflection point on *f*(*x*) is where concavity changes, and concavity is a determined by the slope of the the slopes.

*x* = −3: local minimum*x* = 1: local maximum*x* = −1: inflection point