Q. 27 - 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 $f\text{'} is,$

Step 1. Given Information.

The given graph is,

Step 2. Graph of f '

According to the given graph,

$\text{ The graph of }{f}^{\text{'}}\text{ should be decreasing on }(-\infty ,2)\text{ and increasing on }(2,\infty )\text{, with a local }$minimum at $x=2.$

Step 3. Graph of f .

Now,

The graph of $f$ would be,

$\text{ concave down on }(-\infty ,2)\text{ and concave up on }(2,\infty )\text{ with an inflection point on }x=2\text{. }$