The set of critical value of polynomial functions

Let $f$ be polynomial function: $\mathbb{R^n} \rightarrow \mathbb{R}$. Show that the set of critical values of $f$ is finite.

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Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. If this is homework, please add the homework tag; people will still help, so don't worry. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post. –  Julian Kuelshammer Dec 10 '12 at 19:10
Thanks Richard and Julian Kuelshammer! –  user52523 Dec 10 '12 at 19:16
@user52523 As richard points out, this is not in general true (take a constant function). what extra conditions did you have in mind? –  Alex Youcis Dec 10 '12 at 19:54
I have edited the problem. Thank in advance. –  user52523 Dec 11 '12 at 13:46