Question

use the image to answer the question. which of the following most accurately identifies the relative extrema in the graph? (1 point) there is a relative maximum at (1.5, 0) and (4, 0) and a relative minimum at about (3, 1). there is a relative maximum at (4, 0) and a relative minimum at (3, 1). there is a relative minimum at (4, 0) and a relative maximum at about (3, 1). there is a relative minimum at (4, 0) and a relative maximum at about (3, 1).

Explanation:

Step1: Recall relative - extrema definition

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

Step2: Analyze the graph

Looking at the graph, the function changes from increasing to decreasing around \(x = 3\) and the \(y\) - value at this relative maximum is about \(y = 1\). The function changes from decreasing to increasing around \(x = 4\) and the \(y\) - value at this relative minimum is \(y = 0\).

Answer:

There is a relative minimum at \((4,0)\) and a relative maximum at about \((3,1)\)