Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I was wondering for the bounded function $b(t)$ what statements can be made about the derivative of

$f(t)=exp(b(t))$

specifically it would be nice if the derivative $f'$ were bounded.

share|improve this question
    
Are you assuming $b$ is also differentiable? –  cardinal Jan 25 '12 at 3:11
    
no, just bounded unfortunately. Is there anything I can assume since b(t) is bounded => f(t) is bounded => f' can only be unbounded for limited periods –  user23607 Jan 25 '12 at 3:48
    
See the example I gave in a comment to marty's answer. Nothing about boundedness implies differentiability. Therein lies your problem. –  cardinal Jan 25 '12 at 3:54
    
thanks everyone email from the prof says i can chose b, so this is trivial –  user23607 Jan 25 '12 at 4:34
add comment

1 Answer 1

Only if $b'(t)$ is bounded, since $f'(t) = b'(t) exp(b(t))$.

Try $b(t) = sin(t^2)$.

share|improve this answer
    
I was thinking: Try $b(t) = \log(1 + \chi_{\mathbb{Q}}(t))$. –  cardinal Jan 25 '12 at 3:15
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.