Let $f:M \rightarrow \mathbb{R}$ be a smooth map ($f \in C^{\infty}(M)$), where $M$ is a compact manifold .
Prove that $f^{-1}((-\infty,a])$ is diffeomorphic to $f^{-1}((-\infty,b])$ if the interval $[a,b]$ doesn't contain critical values of $f$.
I have no idea how to deal with this now and really need some hints. Any help would be appreciated.