Question

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

Explanation:

Step1: Recall definitions

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. An absolute maximum is the highest - value point on the entire graph, and an absolute minimum is the lowest - value point on the entire graph.

Step2: Analyze the graph

Looking at the graph, we can see that there is a point where the function changes from decreasing to increasing (relative minimum near \(x = 0\)). There are two points where the function changes from increasing to decreasing (relative maxima). And among the relative maxima, one of them is the highest point on the entire graph (absolute maximum).

Answer:

There is one relative minimum, one relative maximum, and one absolute maximum.