use the given graph of ( f^{prime}(x) ) to find the intervals on which ( f(x) ) is increasing, the intervals…

use the given graph of ( f^{prime}(x) ) to find the intervals on which ( f(x) ) is increasing, the intervals on which ( f(x) ) is decreasing, and the local extrema. sketch a possible graph of ( y = f(x) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the function ( f(x) ) is increasing on (type your answer using interval notation. use a comma to separate answers as needed.) b. there is no solution.

use the given graph of ( f^{prime}(x) ) to find the intervals on which ( f(x) ) is increasing, the intervals on which ( f(x) ) is decreasing, and the local extrema. sketch a possible graph of ( y = f(x) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the function ( f(x) ) is increasing on (type your answer using interval notation. use a comma to separate answers as needed.) b. there is no solution.

Answer

Explanation:

Step1: Recall the relationship between (f^{\prime}(x)) and (f(x))

If (f^{\prime}(x)>0) on an interval (I), then the function (y = f(x)) is increasing on (I). If (f^{\prime}(x)<0) on an interval (I), then the function (y = f(x)) is decreasing on (I).

Step2: Analyze the sign of (f^{\prime}(x)) from the graph

From the graph of (y = f^{\prime}(x)), we can see that (f^{\prime}(x)>0) when (- 2<x<8).

Answer:

A. The function (f(x)) is increasing on ((-2,8))