Q. 24 - Calculus

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

Step-by-Step Solution

Answer

The graph of $f$is,

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

Step 1. Given information.

The graph of $f\text{'}$ is

Step 2. Graph of f .

From the graph,

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

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