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

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) ).\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. ( (-infty,-2),(4,9) )\n(type your answer using interval notation. use a comma to separate answers as needed.)\nb. there is no solution.\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.\n(type your answer using interval notation. use a comma to separate answers as needed.)\nb. there is no solution.

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) ).\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. ( (-infty,-2),(4,9) )\n(type your answer using interval notation. use a comma to separate answers as needed.)\nb. there is no solution.\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.\n(type your answer using interval notation. use a comma to separate answers as needed.)\nb. there is no solution.

Answer

Explanation:

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

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

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

Since (f^{\prime}(x)>0) on ((-\infty,- 2)\cup(4,9)) (given as correct for (f^{\prime}(x)>0)), the function (y = f(x)) is decreasing on the intervals where (f^{\prime}(x)<0). The function (y = f(x)) is decreasing on ((-2,4))

Answer:

For (f^{\prime}(x)<0): A. ((-2,4))