6. Sketch the graph of the function having the given characteristics. f(-6) = f(4) = 0 f'(-2) = f'(1) = 0 f'(x) < 0 if x < -2 f'(x) > 0 if – 2 < x<1 f'(x) < 0 if x >1 f"(x) > 0 if x < -0.5 f"(x) < 0 if x > -0.5

Since f'(x) is a function, f'(x) has its own graph, one that is based on the behavior of f(x). True False

Sketch the graph that possesses the characteristics listed below. f'(-6)=0, f''(-6)<0, f(-6)=3;f'(-2)=0, f''(-2)>0, f(-2)=-3; f''(-4)=0, f(-4)=0

2) If f'(x)=(x-1)²(x-2), where does the graph of f(x) have relative extrema? Justify.