Question

use the graph to answer the following questions.
identify all of the values of c for which ( h(c) ) is a relative maximum of h. if there is more than one value, enter the values as a comma - separated list. if there are none, enter dne.
values:
identify all of the values of c for which ( h(c) ) is a relative minimum of h. if there is more than one value, enter the values as a comma - separated list. if there are none, enter dne.
values:

Explanation:

Step1: Understand the concept of relative maximum

A relative maximum of a function \(y = h(x)\) occurs at a point \(c\) where the function changes from increasing to decreasing. Looking at the graph \(y = h(x)\), we can observe the peak - like points.

Step2: Locate the relative maximum

From the graph \(y=h(x)\), the \(x\) - coordinate of the peak (where the function changes from increasing to decreasing) is \(x = 1\). So, for \(c = 1\), \(h(c)\) is a relative maximum.

Step3: Understand the concept of relative minimum

A relative minimum of a function \(y = h(x)\) occurs at a point \(c\) where the function changes from decreasing to increasing.

Step4: Locate the relative minimum

Looking at the graph \(y = h(x)\), we check the trough - like points. The \(x\) - coordinate of the point where the function changes from decreasing to increasing (in the relevant part of the graph) is \(x=-2\).

Answer:

values for relative maximum: \(1\)
values for relative minimum: \(-2\)