Question

use the graph to determine the following. (a) find the numbers at which f has a relative maximum. what are these relative maxima? (b) find the numbers at which f has a relative minimum. what are these relative minima? (a) the number(s) at which f has a relative maximum is/are - 1 (type an integer or a decimal. use a comma to separate answers as needed.) the relative maximum/maxima is/are 4. (type an integer or a decimal. use a comma to separate answers as needed.) (b) the number(s) at which f has a relative minimum is/are (type an integer or a decimal. use a comma to separate answers as needed.)

Explanation:

Step1: Recall relative - minimum definition

A relative minimum of a function occurs at a point where the function changes from decreasing to increasing.

Step2: Analyze the graph

By observing the given graph, we can see that the function \(y = f(x)\) changes from decreasing to increasing at \(x=-3\) and \(x = 1\). At these points, the \(y\) - values are \(y = 0\).

Answer:

(a) The number(s) at which \(f\) has a relative maximum is/are \(-1\).
The relative maximum/maxima is/are \(4\).
(b) The number(s) at which \(f\) has a relative minimum is/are \(-3,1\).
The relative minimum/minima is/are \(0\).