Trying to find functions with the given property:

Given $M>0, K$ compact in $\mathbf{R^n}$,$f:U\rightarrow\mathbf{R}$ a $C^2$ function, where $U$ open in $\mathbf{R^n}$ and $K\subset U$such that $D^2f_p(h,h)\geq M \times||\triangledown f_p||\times ||h||^2$  $\forall p\in K, h\in\mathbf{R^n}$

Tried many examples. Now, I am not even sure if such a function exists. The main problem is to get the inequality in all the directions. Any help is appreciated.