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 . (type an integer or a decimal. use a comma to separate answers as needed.)

Explanation:

Step1: Recall definition of relative maximum

A relative maximum occurs where the function changes from increasing to decreasing.

Step2: Observe the graph

From the graph, we see the function changes from increasing to decreasing at \(x = 3\). The \(y\) - value at \(x = 3\) is \(y=4\).

Step3: Recall definition of relative minimum

A relative minimum occurs where the function changes from decreasing to increasing.

Step4: Observe the graph again

The function changes from decreasing to increasing at \(x = 1\) and \(x = 5\). The \(y\) - value at \(x = 1\) and \(x = 5\) is \(y = 1\).

Answer:

(a) The number(s) at which \(f\) has a relative maximum is/are \(3\). The relative maximum is \(4\).
(b) The numbers at which \(f\) has a relative minimum are \(1,5\). The relative minima are \(1\).