The condition required for applicability of Rolle's theorem for a real valued function f(x) on an interval [a, b] are :

(A) f is continuous on [a, b]

(B) f is differentiable on (a, b)

(C) f(a) = f(b)

(D) f(c) = 0

Choose the correct answer from the options given below :

(A), (B) and (C) only