Chapter 2, Problem 44RE

(a)

To determine

To graph: For the function $f\text{'}\text{'}$ .

Explanation of Solution

Given information:

The given graph of the derivative $f\text{'}$ of $f$ is shown in figure (1).

  

Figure (1)

Graph:

The graph of $f\text{'}\text{'}$ is positive when $f\text{'}$ is increasing and negative when $f\text{'}$ is negative.

All the local extremes, $f\text{'}\text{'}\left(x\right)=0$ .

The plot for local extremes is shown in figure (2).

  

Figure (2)

The plot for $f\text{'}\text{'}$ is shown in figure (3).

  

Figure (3)

Interpretation: Graph for the function $f\text{'}\text{'}$ is shown in figure (3).

(b)

To determine

To graph: For the function $f$ .

Explanation of Solution

Given information:

The given graph of the derivative $f\text{'}$ of $f$ is shown in figure (1).

  

Figure (1)

Graph:

The function $f$ is snit-derivative of $f\text{'}$ . It has local extremes when $f\text{'}\left(x\right)=0$ .

While it is increases when $f\text{'}\left(x\right)>0$ and decreases when $f\text{'}\left(x\right)<0$ . Start fromleft and the graph of $f$ is shown in figure (4).

  

Figure (4)

Interpretation: Graph for the function $f\text{'}\text{'}$ is shown in figure (4).