Q. 21 - 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

Roots of f' are $x=0,4$ and graph of f' is the following.

The root of f'' is $x=2$and 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 increasing on the interval $\left(-\infty ,0\right).$

f' is decreasing on the interval $\left(0,4\right).$

f' is increasing on the interval $\left(4,\infty \right).$

f' have horizontal tangent at $x=0,4.$ so roots of f' are $x=0,4.$

Step 3. Graph of f''.

Graph of f' state that f'' is decreasing on the interval $\left(-\infty ,2\right).$

f'' is increasing on the interval $\left(2,\infty \right).$

f'' have horizontal tangent at $x=2,$so root of f'' is $x=2.$