### Home > CALC > Chapter 5 > Lesson 5.4.1 > Problem 5-141

5-141.

Given the graph of

*f*′(*x*) below, determine the values of*x*for which*f*(*x*) has local minima, maxima, and points of inflection on the interval [−3, 3]. Homework Help ✎

You are looking at the graph of *f* '(*x*), but you are being asked to describe the graph of *f*(*x*).

A minimum value on *f*(*x*) is where the *y*-values change from decreasing to increasing. How does that show up on the *f* '(*x*) graph?

Local minima on *f*(*x*) are located anywhere that the graph of *f* '(*x*) changes from negative to positive. Local maxima are the reverse.

Points of inflection on *f*(*x*) occur where *f* '(*x*) changes the sign of its slope. This happens twice.