the graph of ( f ) is given.\n(a) on what open intervals is ( f ) increasing?\n(b) on what open intervals is…

the graph of ( f ) is given.\n(a) on what open intervals is ( f ) increasing?\n(b) on what open intervals is ( f ) decreasing?\n(c) what are the ( x )-values of the local minima?\n(d) what are the ( x )-values of the local maxima?\n(a) select the correct choice and, if necessary, fill in the answer box to complete your choice.\na. the function ( f ) is increasing on the open interval(s) \n(type your answer in interval notation. use a comma to separate answers as needed )\nb. there are no open intervals on which the function ( f ) is increasing

the graph of ( f ) is given.\n(a) on what open intervals is ( f ) increasing?\n(b) on what open intervals is ( f ) decreasing?\n(c) what are the ( x )-values of the local minima?\n(d) what are the ( x )-values of the local maxima?\n(a) select the correct choice and, if necessary, fill in the answer box to complete your choice.\na. the function ( f ) is increasing on the open interval(s) \n(type your answer in interval notation. use a comma to separate answers as needed )\nb. there are no open intervals on which the function ( f ) is increasing

Answer

Explanation:

Step1: Recall the relationship between (f') and (f)

If (f'(x)>0) on an open interval (I), then the function (y = f(x)) is increasing on (I).

Step2: Analyze the graph of (f')

Looking at the graph of (y = f'(x)), we find the intervals where (y=f'(x)>0). From the graph, (f'(x)>0) when (x\in(-\infty, - 1)\cup(3,\infty))

Answer:

A. The function (f) is increasing on the open interval(s) ((-\infty,-1),(3,\infty))