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Topic: Does this imply that lim x --> oo f'(x) = 0?
Replies: 18   Last Post: May 26, 2013 1:28 AM

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 steinerartur@gmail.com Posts: 17 Registered: 8/18/12
Re: Does this imply that lim x --> oo f'(x) = 0?
Posted: May 24, 2013 10:31 PM

If inf{f'(x) | x > = 0} > 0, then f(x) --> oo even if f' doesn't have a limit at oo. But if this infimum is 0, then f can have a finite limit at oo. Since f is increasing, the infimum is always >= 0. This can be seen by MVT.

Artur

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