I'm having some trouble with this question:

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- Apr 24th 2010, 10:51 PMacevipaContinuous Functions
I'm having some trouble with this question:

- Apr 24th 2010, 10:57 PMmaddas
This is just the extreme value theorem. Since f is continuous and positive on a compact set [a,b], it achieves a positive minimum in [a,b].

An example of a function for which it fails is on or on . - Apr 24th 2010, 11:03 PMFailure
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.