
Re: Does this imply that lim x > oo f'(x) = 0?
Posted:
May 23, 2013 12:30 PM


On Thu, 23 May 2013 16:24:57 +0100, Robin Chapman <R.J.Chapman@ex.ac.uk> wrote:
>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 ....
In particular, jerks upward very fast, but on a very short interval ("short" interval relative to how fast is fast). Then flat on a very long interval. Then jerks upward even faster, on an even shorter interval...
Showing that f' need not even be bounded.

