proving that f' is bounded

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May 5th 2012, 01:54 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 $-\infty<a<b<\infty$ .

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.

Thanks in advance
May 5th 2012, 02:18 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 $-\infty<a<b<\infty$ .

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.

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