Question

which of the following most accurately identifies the relative maximum and minimum of the polynomial function h(x)? (1 point) there is a relative maximum at x = - 1 and no relative minimum. there is a relative minimum at x = - 1 and a relative maximum at x = 0.25. there is a relative maximum at x = - 1.5 and a relative minimum at x = - 2. there is a relative maximum at x = - 1 and a relative minimum at x = - 0.25.

Explanation:

Step1: Recall relative - extrema definition

A relative maximum occurs where the function changes from increasing to decreasing, and a relative minimum occurs where the function changes from decreasing to increasing.

Step2: Analyze the graph

By observing the graph of the polynomial function, we can see that at \(x = - 1\), the function changes from increasing to decreasing, so there is a relative maximum at \(x=-1\). And there are no points where the function changes from decreasing to increasing in the visible part of the graph, so there is no relative minimum.

Answer:

There is a relative maximum at \(x = - 1\) and no relative minimum.