Question

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

Explanation:

Step1: Recall definition of relative maxima

A relative maximum of a function \(y = f(x)\) occurs at a point \(x = c\) if \(f(c)\geq f(x)\) for all \(x\) in some open - interval containing \(c\). Visually, it is a peak on the graph.

Step2: Examine the graph

Look for the points on the graph where the function changes from increasing to decreasing. These points are the locations of relative maxima.

Step3: Identify the \(x\) - values

Read the \(x\) - coordinates of the relative maxima points from the graph.

Answer:

(Please provide the actual graph for a specific numerical answer. But the general process to find the number(s) at which \(f\) has a relative maximum is as described above. If we assume we have identified the points on the graph, we would write the \(x\) - values here, for example, if the relative maxima occur at \(x = 1\) and \(x = 3\), we would write \(1,3\).)