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

using the given graph of the function f, find the following.\n(a) the numbers, if any, at which f has a local maximum. what are these local maximum values?\n(b) the numbers, if any, at which f has a local minimum. what are these local minimum values?\n(b) find the number(s) x at which f has a local minimum. select the correct choice and, if necessary, fill in the answer box to complete your choice.\na. x = -\\frac{\\pi}{2}\n(type an exact answer, using \\pi as needed. use a comma to separate answers as needed.)\nb. there is no local minimum.\nfind the local minimum value. select the correct choice and, if necessary, fill in the answer box to complete your choice.\na. the local minimum value is\n(type an exact answer, using \\pi as needed. use a comma to separate answers as needed.)\nb. there is no local minimum.

using the given graph of the function f, find the following.\n(a) the numbers, if any, at which f has a local maximum. what are these local maximum values?\n(b) the numbers, if any, at which f has a local minimum. what are these local minimum values?\n(b) find the number(s) x at which f has a local minimum. select the correct choice and, if necessary, fill in the answer box to complete your choice.\na. x = -\\frac{\\pi}{2}\n(type an exact answer, using \\pi as needed. use a comma to separate answers as needed.)\nb. there is no local minimum.\nfind the local minimum value. select the correct choice and, if necessary, fill in the answer box to complete your choice.\na. the local minimum value is\n(type an exact answer, using \\pi as needed. use a comma to separate answers as needed.)\nb. there is no local minimum.

Answer

Explanation:

Step1: Recall the definition of local minimum

A function (y = f(x)) has a local minimum at (x = a) if (f(a)\leq f(x)) for all (x) in some open interval containing (a).

Step2: Analyze the graph

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

Step3: Find the local minimum value

The (y -)coordinate of the point (\left(-\frac{\pi}{2},- 11\right)) gives the local minimum value.

Answer:

  • For the number (x) at which (f) has a local minimum: (x =-\frac{\pi}{2})
  • For the local minimum value: The local minimum value is (-11)