Question

which of the following most accurately identifies the types of extrema in the graph? (8 points) there is one absolute maximum and one relative minimum. there is one relative maximum and one absolute minimum. there is one relative maximum and one relative minimum. there is one relative maximum, one relative minimum, and one absolute minimum.

Explanation:

Step1: Define relative and absolute extrema

A relative maximum is a point where the function changes from increasing to decreasing in a local - neighborhood. A relative minimum is a point where the function changes from decreasing to increasing in a local - neighborhood. An absolute minimum is the lowest point on the entire graph.

Step2: Analyze the graph

Looking at the graph, we can see that there is a point (around \(x = 1\)) where the function changes from increasing to decreasing, which is a relative maximum. There are two points where the function changes from decreasing to increasing, which are relative minima. One of the relative minima is the lowest point on the entire graph, so it is also the absolute minimum.

Answer:

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