# Bounded functions

• Oct 21st 2008, 07:27 PM
EricaMae
Bounded functions
So I just need to clarify the definition of bounded. I'm trying to find a function that is differentiable, f'(x) not bounded. I was thinking of using the natural log function.

ln (x) is differentiable, and I know the graph is not defined at 0. Does that mean that the graph is bounded? Or does bounded just mean bounded above and below?

Thanks!
• Oct 21st 2008, 07:33 PM
kalagota
Quote:

Originally Posted by EricaMae
So I just need to clarify the definition of bounded. I'm trying to find a function that is differentiable, f'(x) not bounded. I was thinking of using the natural log function.

ln (x) is differentiable, and I know the graph is not defined at 0. Does that mean that the graph is bounded? Or does bounded just mean bounded above and below?

Thanks!

yes, boundedness is being bounded above and bounded below..
• Oct 21st 2008, 07:39 PM
EricaMae
So I can say that ln(x) is not bounded, correct?
• Oct 21st 2008, 07:55 PM
kalagota
Quote:

Originally Posted by EricaMae
So I can say that ln(x) is not bounded, correct?

yes.. it is not bounded..
in fact. it is neither bounded above nor bounded below.. however, the domain is bounded below..