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: Analyze local maximum definition

A local maximum of a function occurs at a point where the function value is greater than or equal to the values at nearby points. Looking at the graph, at \(x = 0\), the function \(y=f(x)\) has a higher - value compared to its immediate neighbors.

Step2: Determine the local - maximum value

When \(x = 0\), from the graph, \(y=f(0)=1\).

Answer:

(a) A. The value(s) of \(x\) at which \(f\) has a local maximum is/are \(x = 0\)
(b) A. The local maxima is/are \(y = 1\)