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 = (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.

Explanation:

Step1: Recall local - maximum definition

A local 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 \(c\).

Step2: Examine the graph

Looking at the graph of the function, we see that at \(x = 0\), the function value \(f(0)=1\) and for \(x\) values in an open - interval around \(x = 0\), \(f(x)\leq f(0)\).

Answer:

A. The value(s) of x at which f has a local maximum is/are \(x = 0\)