# Math Help - Differentiability implies linearity question

1. ## Differentiability implies linearity question

Hello, my problem is:

Let $f: R^m \to R$ differentiable and $f(x/2) = f(x)/2$ for all $x \in R^m$. Prove that f is linear.

I think the aswer involves the gradient, but I don't know why.

2. ## Re: Differentiability implies linearity question

differentiate the equation, we got f'(x/2)/2=f'(x)/2, so f'(x)=f'(x/2)=...=f'(0) is constant.