Question

use the graph of the function f given below to answer the questions. is there a local maximum at x = 2? yes no if there is a local maximum at x = 2, what is it? select the correct choice below and fill in any answer boxes within your choice. a. the local maximum is y = (type an integer.) b. there is no local maximum at x = 2.

Explanation:

Step1: Recall the definition of local maximum

A local maximum of a function \(y = f(x)\) at a point \(x = a\) is a point where the function value \(f(a)\) is greater than or equal to the function values in some open interval containing \(a\).

Step2: Analyze the graph at \(x = 2\)

Looking at the graph, at \(x = 2\), the function has a peak. The \(y\) - coordinate of this peak is \(4\).

Answer:

A. The local maximum is \(y = 4\)