Question

use the graph to find:
(a) the numbers, if any, at which f has a local maximum. what are these local maxima?
(b) the numbers, if any, at which f has a local minimum. what are these local minima?
(a) select the correct choice below and fill in any answer boxes within your choice.
a. the value(s) of x at which f has a local maximum is/are
x = 0.
(type an integer. use a comma to separate answers as needed.)
b. there are no values of x at which f has a local maximum.
select the correct choice below and fill in any answer boxes within your choice.
a. the local maxima is/are y=
(type an integer. use a comma to separate answers as needed.)
b. there are no local maxima.

Explanation:

Step1: Recall the definition of local maximum

A local maximum of a function \(y = f(x)\) occurs at a point \(x = a\) if \(f(a)\geq f(x)\) for all \(x\) in some open interval containing \(a\). From the graph, when \(x = 0\), the \(y\) - value is \(y=3\).

Step2: Determine the local maxima value

Since the \(y\) - coordinate of the local maximum (where \(x = 0\)) is \(y = 3\)

Answer:

A. The local maxima is/are \(y = 3\)