Hi forum. I'm trying to prove a claim from Mathematical Analysis I - Zorich since some days, but I succeeded only in part. The complete claim is: \left\{\begin{matrix} f\in\mathcal{C}^{(n)}(-1,1) \\ \sup_{x\in (-1,1)}|f(x)|\leq 1 \\ |f'(0)|>\alpha _n \end{matrix}\right. \Rightarrow \exists...