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) ). on what subinterval(s) is ( f(x)>0 )? select the correct choice below and, if necessary, fill in the answer box to complete your choice

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) ). on what subinterval(s) is ( f(x)>0 )? select the correct choice below and, if necessary, fill in the answer box to complete your choice

Answer

Explanation:

Step1: Recall the relationship between the function and its derivative

If (y = f(x)) is increasing on an interval, then (f^{\prime}(x)>0) on that interval. If (y = f(x)) is decreasing on an interval, then (f^{\prime}(x)<0) on that interval. The values of (x) for which (f^{\prime}(x) = 0) are the (x -)coordinates of the local maxima and minima of (y=f(x)).

Step2: Analyze the graph of (y = f(x)) for increasing intervals

Looking at the graph of (y = f(x)), we observe that the function (y=f(x)) is increasing on the intervals ((-5,-3)) and ((-1,3))

Answer:

(f^{\prime}(x)>0) on the intervals ((-5,-3)) and ((-1,3))