Question

find the absolute extreme values and where they occur.
select the correct choice below and, if necessary, fill in the answer boxes within your choice.
a. the absolute maximum value is at ( x = ) there is no absolute minimum value.
b. the absolute minimum value is at ( x = ). there is no absolute maximum value.
c. the absolute maximum value is at ( x = ), and the absolute minimum value is at ( x = ).
d. there is no absolute maximum value or absolute minimum value.

Explanation:

Step1: Analyze the graph

From the graph, we can see that the left - hand endpoint is a closed point (a solid dot), and the right - hand endpoint is an open point (a hollow dot).

Step2: Determine the absolute maximum

The absolute maximum occurs at the left - hand endpoint. By looking at the coordinates of the closed point, we can find its \(y\) - value and \(x\) - value. The closed point has coordinates \((- 6,-4)\).

Answer:

A. The absolute maximum value is \(-4\) at \(x = - 6\). There is no absolute minimum value.