differentiability and compactness I have no idea how to show whether this statement is false or true:

If every differentiable function on a subset $X\subseteq\mathbb{R}^n$ is bounded then $X$ is compact.

Thank you

Some hints:


*

*By the Heine-Borel property for Euclidean space, $X$ is compact if and only if $X$ is closed and bounded. 

*My inclination is to prove the contrapositive: If $X$ is not compact, then there exists a differentiable function on $X$ which is unbounded.

*If $X$ is not compact, then either it isn't bounded, or it isn't closed. As a first step, perhaps show why the contrapositive statement must be true if $X$ isn't bounded?

