I'm having some trouble with this question:
How you go about proving this much depends on what you already know about compact intervalls like [a;b], and continuous functions.
For example, there is a theorem that says that for a continuous function on a compact interval [a;b], there are , such that , for all .
So, if you can use that theorem, you can just put , but if you cannot use that theorem, you have to (essentially) prove it.