If the functions f and g are defined for all real numbers and f is an antiderivative of g, which of the following statements is NOT necessarily true? O (A) If g (a) > 0 for all x, then f is increasing. O (B) If g (a) = 0, then the graph of f has a horizontal tangent at a = a. O (C) If f (ac) = 0 for all a, then g (a) = 0 for all ac. (D) If g (x) = 0 for all ac, then f (ac) = 0 for all a. O (E) f is continuous for all z