Use l'Hôpital's rule...
I've been rooting around for a counterexample in vain so I think this is true.Suppose that 0, \infty) \rightarrow \mathbb{R}" alt="f0, \infty) \rightarrow \mathbb{R}" /> is twice differentiable and .
Is it true that ?
However, I have no idea how to prove it is true!
Does anyone have any ideas?
I've already tried using L'Hopital's rule and it got me nowhere.
Here's what I did:
Suppose this tends to a limit a where .
So L' Hopital's rule applies.
Therefore since
However this contradicts our definition of a!