using the given graph of the function f, find the following. (a) the numbers, if any, at which f has a local…

using the given graph of the function f, find the following. (a) the numbers, if any, at which f has a local maximum. what are these local maximum values? (b) the numbers, if any, at which f has a local minimum. what are these local minimum values? (a) find the value(s) of x at which f has a local maximum. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. x = □ (type an exact answer, using π as needed. use a comma to separate answers as needed.) b. there is no local maximum value.

using the given graph of the function f, find the following. (a) the numbers, if any, at which f has a local maximum. what are these local maximum values? (b) the numbers, if any, at which f has a local minimum. what are these local minimum values? (a) find the value(s) of x at which f has a local maximum. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. x = □ (type an exact answer, using π as needed. use a comma to separate answers as needed.) b. there is no local maximum value.

Answer

Explanation:

Step1: Recall local - maximum and minimum definitions

Local maximum is a point where the function value is greater than or equal to the values at nearby points, and local minimum is a point where the function value is less than or equal to the values at nearby points.

Step2: Analyze the graph

From the graph, we can see that the function has a local maximum at (x =-\frac{\pi}{2}) and (x=\frac{\pi}{2}), and a local minimum at (x = \pi) and (x=-\pi).

Answer:

(a) A. (x =-\frac{\pi}{2},\frac{\pi}{2}) (b) The numbers at which (f) has a local minimum are (x =-\pi,\pi)