Please explain option a&b

EQunCIE Suppose f: R->R is a function that satisfies |f(x) - f(y)| x - ylP, B > 0. Which of the following 19. is correct ? (A) if B = 1 then f is differentiable (B) f must be a polynomial (C) if B> 1 then f is a constant function (D) None of these