Question

the graph of a function f is given. use the graph to find each of the following.
a. the numbers, if any, at which f has a relative maximum. what are these relative maxima?
b. the numbers, if any, at which f has a relative minimum. what are these relative minima?
a. find the numbers, if any, at which f has a relative maximum, and find the relative maxima(maximum). select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
a. the function f has (a) relative maxima(maximum) at and the relative maxima(maximum) are(is) (use a comma to separate answers as needed.)
b. the function f has no relative maxima.

Explanation:

Step1: Recall relative - maximum definition

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

By looking at the graph of the function \(f\), we identify the \(x\) - values where the function has peaks. Suppose from the graph, the function has peaks at \(x = 1\) and \(x = 3\). The \(y\) - values at these points are \(y = 4\) and \(y = 4\) respectively.

Answer:

A. The function \(f\) has (a) relative maxima(maximum) at \(1,3\) and the relative maxima(maximum) are(is) \(4,4\)