sketch the graph

Question

4) Sketch the graph of a function that satisfies all of the given conditions. f^ prime (0)=f^ prime (5)=0 f^ prime (x)=1 if x<-2 f^ prime (x)>0 if 0<3 0 < x < 3 f^ prime (x)<0 if-2< - 2 < x < 0 or 3 < x < 5 or x > 5 lim x 3^ - f(x)= infty lim x 3^ + f(x)= infty f^ prime prime (x)>0 it-2< - 2 < x < 3 or 3 < x < 5 f^ prime prime (x)<0 x > 5

Answer 1

How about this:

A sharp point at x = -2 and x = 3. A normal minimum at x = 0. A point of inflection at x = 5