SOLUTION: Sketch the graph of the function f(x) that satisfies f'(x)>0 for x<-2 and x>3 and f'(x)<0 for -2<x<3

I admonish your word "the", since there are billions of quadrillions of possible
functions, in fact an infinite number of different functions that would satisfy
those conditions.  You should use "a", not "the". 

Here is one of many, many possibilities.



It's going up to the left of 2 and right of 3 on the x-axis.
It's going down between 2 and 3 on the x-axis

Edwin