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: Identify relative maxima x-values

Look for peaks on the graph; the peaks occur at $x=-1$ and $x=3$.

Step2: Identify relative maxima y-values

The y-value (function value) at both peaks is $4$.

Step3: Identify relative minima x-values

Look for valleys on the graph; the valley occurs at $x=1$.

Step4: Identify relative minima y-values

The y-value (function value) at the valley is $0$.

Answer:

Part a:

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

Part b:

The function f has a relative minimum at $\boldsymbol{1}$ and the relative minimum is $\boldsymbol{0}$.