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Topic: Unbounded second derivative
Replies: 4   Last Post: Dec 4, 2012 7:00 AM

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Jose Carlos Santos

Posts: 4,896
Registered: 12/4/04
Unbounded second derivative
Posted: Dec 3, 2012 6:17 AM
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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

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