use the graph to find: (a) the numbers, if any, at which f has a local maximum. what are these local maxima…

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 = - 2 (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. (b) 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 minimum is/are x = 0 (type an integer. use a comma to separate answers as needed.) b. there are no local minima.

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 = - 2 (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. (b) 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 minimum is/are x = 0 (type an integer. use a comma to separate answers as needed.) b. there are no local minima.

Answer

Explanation:

Step1: Recall local - maximum and minimum definitions

A local maximum of a function (y = f(x)) occurs at a point (x = c) if (f(c)\geq f(x)) for all (x) in some open interval containing (c). A local minimum of a function (y = f(x)) occurs at a point (x = c) if (f(c)\leq f(x)) for all (x) in some open interval containing (c).

Step2: Analyze the given graph

Looking at the graph, at (x=-2), the function value (y = f(-2)) is greater than the function values in a small open - interval around (x = - 2). So (x=-2) is a point of local maximum.

Step3: Check for local minimum

At (x = 0), the function value (y = f(0)) is less than the function values in a small open - interval around (x = 0). So (x = 0) is a point of local minimum.

Answer:

(a) A. The value(s) of (x) at which (f) has a local maximum is/are (x=-2) (b) A. The value(s) of (x) at which (f) has a local minimum is/are (x = 0)