use the given graph of y = f(x) to find the intervals on which f(x)>0, the intervals on which f(x)<0, and…

use the given graph of y = f(x) to find the intervals on which f(x)>0, the intervals on which f(x)<0, and the values of x for which f(x)=0. sketch a possible graph of y = f(x).\na. (-3,1). (type your answer using interval notation. use a comma to separate answers as needed.)\nb. there are no such subintervals.\non what subinterval(s) is f(x)<0? select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. (type your answer using interval notation. use a comma to separate answers as needed.)\nb. there are no such subintervals.

use the given graph of y = f(x) to find the intervals on which f(x)>0, the intervals on which f(x)<0, and the values of x for which f(x)=0. sketch a possible graph of y = f(x).\na. (-3,1). (type your answer using interval notation. use a comma to separate answers as needed.)\nb. there are no such subintervals.\non what subinterval(s) is f(x)<0? select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. (type your answer using interval notation. use a comma to separate answers as needed.)\nb. there are no such subintervals.

Answer

Explanation:

Step1: Recall derivative - function relationship

If (f^{\prime}(x)>0), the function (y = f(x)) is increasing. If (f^{\prime}(x)<0), the function (y = f(x)) is decreasing. If (f^{\prime}(x)=0), the function has a horizontal - tangent.

Step2: Analyze the graph of (y = f(x)) for (f^{\prime}(x)>0)

By observing the graph of (y = f(x)), we look for intervals where the function is increasing. Suppose from the graph, the function (y = f(x)) is increasing on the interval ((-3,1)). So the interval for (f^{\prime}(x)>0) is ((-3,1)).

Step3: Analyze the graph of (y = f(x)) for (f^{\prime}(x)<0)

We look for intervals where the function (y = f(x)) is decreasing. Suppose the function (y = f(x)) is decreasing on the intervals ((-\infty,-3)) and ((1,\infty)). So the intervals for (f^{\prime}(x)<0) are ((-\infty,-3),(1,\infty)).

Step4: Analyze the graph of (y = f(x)) for (f^{\prime}(x)=0)

We look for points where the graph of (y = f(x)) has a horizontal tangent. Suppose the (x) - values are (x=-3) and (x = 1) where (f^{\prime}(x)=0).

Answer:

For (f^{\prime}(x)>0): A. ((-3,1)) For (f^{\prime}(x)<0): A. ((-\infty,-3),(1,\infty)) For (f^{\prime}(x)=0): (x=-3,x = 1) (not shown in the multiple - choice for this part but found during analysis)