Q. 25 - 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 $f is,$

The graph of $f\text{'}\text{'} is,$

Step 1. Given Information.

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

Step 2. Graph of f .

According to the given graph,

$$\begin{gathered} f<0, when interval is (-3,0) \\ f>0, when interval is (-\infty ,-3),(0,\infty ) \\ Roots: x=0,-3 \end{gathered}$$

Thus, the graph will be,

Step 3. Graph of f ' ' .

As per the given graph, the graph of $f\text{'}\text{'}$ will be,