Let $$f : R \rightarrow R$$ be a function such that
$$f(x + y) = f(x) + f(y), \forall x, y \in R$$
If f(x) is differentiable at x = 0, Then

A

f(x) is differentiable only in a finite interval containing zero

B

f(x) is continuous $$\forall x \in R$$

C

f '(x) is constant $$\forall x \in R$$

D

f(x) is differentiable except at finitely many points