I have asked too many hard questions recently now an easy one.

Let $\displaystyle f: [a,b] \rightarrow \mathbb{R} $ be continuous. Then $\displaystyle \exists u,v \in [a,b] $ such that $\displaystyle f(u) \le f(x) \le f(v) $ for all $\displaystyle x \in [a,b]$.

What if we have a function going to a subset of R, e.g. [-6, 7] or something, can we still use the EVT?