Chapter 3.6, Problem 17E

To determine

To locate: name and classify the extrema of the function.

Answer to Problem 17E

Absolute minimum point = $\left(3,-8\right)$

Relative minimum point = $\left(8,-5\right)$

Relative maximum point = $\left(5,-2\right)$

Explanation of Solution

Given information:

The graph of $y=f\left(x\right)$ is as follows:

  

Calculation:

At $x=3\text{ and }8$ , the graph is decreasing on the left and increasing on the right. The values of relative minimum are $\left(8,-5\right)\text{ and }\left(3,-8\right)$ . Since, the lowest value in the graph is at $\left(3,-8\right)$ so this is the absolute minimum value, and $\left(8,-5\right)$ is relative minimum value.

At $x=5$ , the graph is decreasing on the right and increasing on the left. The value of relative maximum point is $\left(5,-2\right)$ .