Q1 15 pts]: Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. (a) If f'(c) = 0, then f has a local maximum or a local minimum at c. (b) Iff' (x) = g' (x) for x in (3,12), then f(x) = g(x) for x in (3,12). (c) The point (c, f(c)) is a point of inflection if f"(c) = 0. (d) The function f(x) = x3 + 3x has no local maximum or local minimum values. (e) If f(2) = f(5) = 7 then there is a number c in (2,5) such that f'(c) = 0.