Ok, here it goes the problem:
Let $f:U\rightarrow\mathbb{R}$ a function that belongs to $C^2(U)$ (i.e. the second partial derivatives of $f$ are continuous), where $U$ is an open subset of $\mathbb{R}^n.$ How can I prove that for every $K\subset U$ is a compact subset of $\mathbb{R}^n,$ there is a constant $C_K>0$ such that \begin{equation} |f(x+h)-f(x)-h\cdot\nabla f(x)|\leq C_K|h|^2 \end{equation} for every $x\in K$ and $|h|\leq1?$