Mathematics

Problem

Let

f(x+y) = f(x) + f(y)

and

f(x) = x^2 g(x)

for all

x, y \in \mathbb{R}

, where

g(x)

is continuous function. Then

f'(x)

is equal to (a)

g'(x)

(b)

g(0)

(c)

g(0) + g(x)

(d) 0