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: Understand relative maximum

A relative maximum of a function \(y = f(x)\) occurs at a point \(x = a\) if \(f(a)\geq f(x)\) for all \(x\) near \(a\). Visually, it is a "peak" on the graph.
Looking at the graph, we can see that there is a peak at \(x=-1\). The \(y -\) value (the value of the function) at \(x =- 1\) is \(y = 3\).

Answer:

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