Answer Happy

2. Let f and g be functions which are differentiable on R. For each of the following statements, determine if it is true or false. If it is true, then prove it. If it is false, then give a counterexample (you must prove that it is indeed a counterexample). (a) If f'(x) = g'(x) for all x, then f(0) = g(0). O True O False

(b) If f'(x) > sin(x) + 2 for all x ≤ R, then there is no solution to the equation ef(ª) = 1. True O False

(c) If f is strictly increasing and g is strictly decreasing, then both fog and go f are strictly decreasing. O True O False