proving that f' is bounded

The problem I am trying to solve is

is a differentiable function and it has a continuous derivative. I need to prove that is bounded on where .

I have shown that if is continous on and if is a compact subset of that is also compact. But have no clue if this will help of where to go from here.

Thanks in advance

Re: proving that f' is bounded

Quote:

Originally Posted by

**klw289** The problem I am trying to solve is

is a differentiable function and it has a continuous derivative. I need to prove that

is bounded on

where

.

I have shown that if

is continous on

and if

is a compact subset of

that

is also compact. But have no clue if this will help of where to go from here.

It tells you "it has a __continuous__ derivative..

Any continuous function is bounded on a compact set.

Any interval is compact.