Question

values of all relative extrema for the function with the graph below.
the function has a relative
the function has a relative
at ( x=)
at ( x=)

Explanation:

Step1: Recall the definition of relative extrema

A relative maximum is a point where the function changes from increasing to decreasing. A relative minimum is a point where the function changes from decreasing to increasing.

Step2: Analyze the graph

Looking at the graph, at \(x = - 2\), the function changes from increasing to decreasing. So, the function has a relative maximum at \(x=-2\). At \(x = 2\), the function changes from decreasing to increasing. So, the function has a relative minimum at \(x = 2\).

Answer:

The function has a relative maximum at \(x=-2\) and a relative minimum at \(x = 2\).