Question

In Exercises $21-28$, graphs of $f,f\text{'}$, or $f\text{'}\text{'}$are given. Whichever is shown, sketch graphs of the remaining two functions. Label the locations of any roots, extrema, and inflection points on each graph

Short answer

The graph of $f$is,

and the graph of $f\text{'}\text{'}$is,

Step-by-step solution

Step 1. Given information.

The graph of $f\text{'}$is

Step 2. Graph of f.

From the graph,

$$\begin{gathered} f<0,whenintervalis(-\infty ,0)and(2,\infty ). \\ f>0,whenintervalis(0,2) \\ Roots:x=0,2 \end{gathered}$$

Therefore, the graph will be,

Step 3. Graph of f''.

It is clear from the given graph that the graph of $f\text{'}\text{'}$will be