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 concept

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

Step2: Observe the graph

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