Hello, my problem is:
Let $\displaystyle f: R^m \to R$ differentiable and $\displaystyle f(x/2) = f(x)/2$ for all $\displaystyle x \in R^m$. Prove that f is linear.
I think the aswer involves the gradient, but I don't know why.
Hello, my problem is:
Let $\displaystyle f: R^m \to R$ differentiable and $\displaystyle f(x/2) = f(x)/2$ for all $\displaystyle x \in R^m$. Prove that f is linear.
I think the aswer involves the gradient, but I don't know why.