Question

the x - values, if any, where f has a relative maximum. the value(s), if any, of the relative maximum(s) of f. the x - values, if any, where f has a relative minimum. the value(s), if any, of the relative minimum(s) of f. the x - value(s) at which the function has a relative maximum is/are: one or more solutions: no solution the relative maximum/maxima are: one or more solutions:

Explanation:

Step1: Recall relative - maximum concept

A relative maximum occurs where the function changes from increasing to decreasing.

Step2: Analyze the graph

Looking at the graph, the function changes from increasing to decreasing at \(x=- 1\).

Step3: Find the relative - maximum value

When \(x = - 1\), the \(y\) - value of the function is \(-4\).

Step4: Recall relative - minimum concept

A relative minimum occurs where the function changes from decreasing to increasing.

Step5: Analyze the graph for relative - minimum

The function changes from decreasing to increasing at \(x=-3\).

Step6: Find the relative - minimum value

When \(x=-3\), the \(y\) - value of the function is \(-6\).

Answer:

The \(x\) - value(s) at which the function has a relative maximum is/are: \(x=-1\)
The relative maximum/maxima are: \(y = - 4\)
The \(x\) - value(s) at which the function has a relative minimum is/are: \(x=-3\)
The relative minimum/minima are: \(y=-6\)