CPM Homework Help : CALC Problem 5-141

Given the graph of $f^\prime(x)$ below, determine the values of $x$ for which $f(x)$ has local minima, maxima, and points of inflection on the interval $[−3, 3]$ .

Hint 1:

You are looking at the graph of $f^\prime(x)$ , but you are being asked to describe the graph of $f(x)$ .

Hint 2:

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

Hint 3:

Local minima on $f(x)$ are located anywhere that the graph of $f^\prime(x)$ changes from negative to positive. Local maxima are the reverse.

Hint 4:

Points of inflection on $f(x)$ occur where $f^\prime(x)$ changes the sign of its slope. This happens twice.