Continuity - minimum and maximum

Hi. I'd really appreciate any help you can give me on this.

If is a continuous, periodic function, then prove has a maximum and minimum.

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A periodic function is where if you have any K>0, then for all , . And we need to show that a set has a maximum and minimum.

I'm thinking that we need to show it is bounded first of all. But I have no idea how I could do that. I'm just jotting down some thoughts, so I don't know whether they are relevant.

for all

This question in the textbook is under the section of the "The extreme value theorem" so I think that must be relavent.

Please help. (Doh)

Regards,

Joel.