Let f: R ® R be a function such that f(x + y) = f(x) + f(y), " x, y Î 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 " x Î R
(C) f¢(x) is constant " x Î R
(D) f(x) is differentiable except at finitely many points