# proving that f' is bounded

• May 5th 2012, 02:54 PM
klw289
proving that f' is bounded
The problem I am trying to solve is
$f:\Re\rightarrow\Re$ is a differentiable function and it has a continuous derivative. I need to prove that $f'$ is bounded on $[a,b]$ where $-\infty.

I have shown that if $f:X\rightarrow Y$ is continous on $X$ and if $A$ is a compact subset of $X$ that $f(A)$ is also compact. But have no clue if this will help of where to go from here.

• May 5th 2012, 03:18 PM
Plato
Re: proving that f' is bounded
Quote:

Originally Posted by klw289
The problem I am trying to solve is
$f:\Re\rightarrow\Re$ is a differentiable function and it has a continuous derivative. I need to prove that $f'$ is bounded on $[a,b]$ where $-\infty.

I have shown that if $f:X\rightarrow Y$ is continous on $X$ and if $A$ is a compact subset of $X$ that $f(A)$ 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 $[a,b]$ is compact.