Sketch the graph of a function that is:

a) Differentiable on (-5,1) and (1,5) and not differentiable at 5.

b) f'(x)<0 on (-5,1)

c) f"(x)=0 when x=3, f"(x)>0 on (1,3), f"(x)<0 on (3,5)

d) f is continuous at x=1

e) f(-4)=3, f(-1)=-2

f) Prove that f has one and only one zero on the interval (-5,1).