Let be a function that maps closed and bounded intervals onto closed and bounded intervals, hence if , then for some real numbers .
1)Prove that there is an contained in such that for all contained in
2)Prove the range of has the intermediate value propery.
3)Give an example showing not needing to be continuous.
1) It would appear that we are looking for an upper bound for ? I'm not reall too sure how to start that one though...
2) Well, possibly we can define and and then use that for , . Then show that is between ???
3)I think I can probably take a better guess once I have a better understand of 1) and 2)
Any help would be greatly appreciated.