# Proving linearity from diferentiability

I dont know how to prove that if $f: \mathbb{R}^{n} \rightarrow \mathbb{R}$ is diferentiable and $f(x/2) = f(x)/2$ for all $x \in \mathbb{R}^n$ then $f$ is linear. Anyone could give me a hint?

• list out all the definitions for diffrentiable, linear. and it should help – shai horowitz May 23 '16 at 1:48
• Maybe take the gradient and you can show each component is a constant function. Just a thought, I'm not certain that solves it. – jdods May 23 '16 at 1:49