Q. 22 - Calculus

Question

In Exercises 21–28, graphs of f, f', or f'' 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 following. 

The graph of f'' is the following. 

Step 1. Given information.

The given graph of f is the following. 

Step 2. Graph of f'.

Graph of f state that the f' is decreasing on the interval $\left(-\infty ,-1\right).$

then again f' is decreasing on the interval $\left(-1,\infty \right).$

so graph of f' is following.

Step 3. Graph of f''.

Graph of f' state that f'' is increasing on the interval $\left(-\infty ,-1\right)$

f'' is decreasing on the interval $\left(-1,\infty \right).$

So the graph of the f'' is following.