Determine whether the following statements are true or false.

If a statement is true, then explain why using definitions and/or theorems.

If a statement is false, then provide a counterexample. Your counterexample may be either the

graph of the function or the analytical definition

A) If limx5f(x) does not exist, then limx5(f(x))2 does not exist

B) Suppose f'' is continuous on (- , ) if f'(-2) = 0 and f''(-2) < 0, then f must achieve both an absolute and local maximum at x = - 2

C) Suppose we know that a particle is speeding up on the interval (0 , 5) and slowing down

on the interval (5 , 7). It is possible for the particle to be moving forward on both (0, 5) and (5, 7)

D) If f is a continuous function defined on (- , ) such that f(x) > 0 for all x, then (f(x))2dx=(f(x)dx)2