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 number(s) x at which f has a local maximum. select the correct choice 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.

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 number(s) x at which f has a local maximum. select the correct choice 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.

Answer

Explanation:

Step1: Recall the definition of local maximum

A function (y = f(x)) has a local maximum at a point (x = a) if (f(a)\geq f(x)) for all (x) in some open interval containing (a). Geometrically, it is a "peak" on the graph of the function.

Step2: Analyze the given graph

Looking at the graph of the function (y = f(x)), we can observe the point ((\frac{\pi}{2},11)). For values of (x) in an open interval around (x=\frac{\pi}{2}), the function value (f(x)) at (x = \frac{\pi}{2}) is greater than the function values (f(x)) for other (x) in that open - interval.

Answer:

A. (x=\frac{\pi}{2})