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.

If $a<b$, what qualities of $f(x)$ are needed to be certain that $f(a) < f(b)$ ? For example, is it enough to say that $f(x)$ is monotonic and positive?

share|improve this question
2  
Perhaps you are confusing monotonicity with the fact that if the derivative is positive, then the function is strictly increasing. –  Srivatsan Sep 23 '11 at 16:41

1 Answer 1

up vote 1 down vote accepted

If you need this for all $a$ and $b$ then by definition $f$ is strictly increasing. Being positive is not relevant.

share|improve this answer

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.