Chapter 4.3, Problem 23E

a.

To determine

To find the increasing interval in the graph

Answer to Problem 23E

The interval is $(-\infty ,2]\text{ and }[0,2]$

Explanation of Solution

Given:

The graph of the function $f\text{'}$ is given

  

Calculation:

The function f $f$ is increasing, where $f\text{'}$ is positive, that is in the interval $(-\infty ,2]\text{ and }[0,2]$ .

b.

To determine

To find the decreasing interval in the graph

Answer to Problem 23E

The interval is $[-2,0]\text{ and }[2,\infty )$ .

Explanation of Solution

Given:

The graph of the function $f\text{'}$ is given

  

Calculation:

The function f $f$ is decreasing, where $f\text{'}$ is negative, that is in the interval $[-2,0]\text{ and }[2,\infty )$ .

c.

To determine

To find the local maximum and local minimum in the graph.

Answer to Problem 23E

Local maxima at $x=-2\text{ and }x=2$ and local minimum at $x=0$ .

Explanation of Solution

Given:

The graph of the function $f\text{'}$ is given

  

Calculation:

Local maxima at $x=-2\text{ and }x=2$ .

Local minimum at $x=0$ .