Let $g:C\to \mathbb{R}$ be a function with the property $\exists A>0 \exists \alpha >1 \forall x\in C : |g(x)|\leq A\cdot|x|^\alpha$. $C$ is a circle with a radius radius $r>0$ with its center point in 0,0.
Now I want to proof, that $g$ is differentiable in $0$. Could you give me a hint, how I could solve this problem?