CPM Homework Help : CALC Problem 5-98

Using the graph of $f^\prime(x)$ , determine the values of $x$ where $f(x)$ has a local minimum, local maximum or point of inflection. Justify your answer for each point.

Hint 1:

You are looking at a graph of $f^\prime(x)$ , which shows all the slopes of $f(x)$ .

Hint 2:

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

Hint 3:

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

Hint 4:

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

Answer:

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