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.
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)