Chapter 4.3, Problem 48E

a.

To determine

To find the increasing interval in the graph

Answer to Problem 48E

The interval is $\text{[0,3]}$

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 $\text{[0,3]}$ .

b.

To determine

To find the decreasing interval in the graph

Answer to Problem 48E

The interval is nowhere.

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 nowhere.

c.

To determine

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

Answer to Problem 48E

Local maxima at $x=3$ .

Local minimum at $x=0$ .

Explanation of Solution

Given:

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

  

Calculation:

Local maxima at $x=3$ .

Local minimum at $x=0$ .