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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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Robin Chapman

Posts: 257
Registered: 5/29/08
Re: Does this imply that lim x --> oo f'(x) = 0?
Posted: May 23, 2013 11:24 AM
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On 23/05/2013 16:11, steinerartur@gmail.com wrote:
> Suppose f:[0, oo) --> R is increasing, differentiable and has a
> finite limit as x --> oo. Then, must we have lim x --> oo f'(x) = 0?
> I guess not, but couldn't find a counter example.


Think of a function that's flat, then rapidly jerks upward then
flat again then rapidly jerks up and does this infinitely
often ....




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