I have just recently covered the Intermediate Value Theorem, and I wanted to practice solving problems involving this theorem. However, I encountered a problem that I am not exactly sure how to tackle (it's a question involving a periodic function).
I thought about splitting the proofs into 3 cases, but I don't think it would be applicable here?
The question is:
If f is periodic with a period of 2a for some , then for all . Show that if f is continous, there exists some such that .
Any help would be greatly appreciated. Thanks a lot!