Date: Dec 3, 2012 6:17 AM
Author: Jose Carlos Santos
Subject: Unbounded second derivative

Hi all,

This is probably very simple, but I can't see it. :-) Let f be a twice
derivable function from [0,+oo[ into R such that:

1) lim_{x to +oo} f(x) = 0;

2) lim_{x to +oo} f'(x) does not exist.

Prove that the function f'' is unbounded.

Best regards,

Jose Carlos Santos