use the graph to determine the following. (a) find the numbers at which f has a relative maximum. what are…

use the graph to determine the following. (a) find the numbers at which f has a relative maximum. what are these relative maxima? (b) find the numbers at which f has a relative minimum. what are these relative minima? (a) the number(s) at which f has a relative maximum is/are . (type an integer or a decimal. use a comma to separate answers as needed.)

use the graph to determine the following. (a) find the numbers at which f has a relative maximum. what are these relative maxima? (b) find the numbers at which f has a relative minimum. what are these relative minima? (a) the number(s) at which f has a relative maximum is/are . (type an integer or a decimal. use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Recall relative - maximum definition

A function (y = f(x)) has a relative maximum at (x = c) if (f(c)\geq f(x)) for all (x) in some open interval containing (c). Looking at the graph, we observe the peaks.

Step2: Identify relative - maximum points

From the graph, the function (f(x)) has a relative maximum at (x=- 1). The value of the function at (x = - 1) is (f(-1)=4).

Step3: Recall relative - minimum definition

A function (y = f(x)) has a relative minimum at (x = c) if (f(c)\leq f(x)) for all (x) in some open interval containing (c). Looking at the graph, we observe the valleys.

Step4: Identify relative - minimum points

From the graph, the function (f(x)) has relative minima at (x=-3) and (x = 1). The values of the function at these points are (f(-3)=1) and (f(1)=1).

Answer:

(a) The number(s) at which (f) has a relative maximum is/are (-1). The relative maximum is (4). (b) The numbers at which (f) has a relative minimum are (-3,1). The relative minima are (1,1).