Question

which of the following most accurately identifies the types of extrema in the graph? (1 point) there is one relative maximum and one relative minimum. there is one relative maximum, one relative minimum, and one absolute minimum. there is one absolute maximum and one relative minimum. there is one relative maximum and one absolute minimum.

Explanation:

Step1: Identify 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. From the graph, we can see a relative maximum near \(x = 1.5\) and a relative minimum near \(x=5\).

Step2: Identify absolute extrema

The absolute minimum is the lowest - value point of the function over its entire domain shown. The lowest point of the graph in the given domain is the relative minimum near \(x = 5\), and there is no absolute maximum shown as the graph goes up on both ends.

Answer:

There is one relative maximum and one relative minimum.