The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
David C. Ullrich

Posts: 3,555
Registered: 12/13/04
Re: Does this imply that lim x --> oo f'(x) = 0?
Posted: May 23, 2013 12:30 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Thu, 23 May 2013 16:24:57 +0100, Robin Chapman
<> wrote:

>On 23/05/2013 16:11, 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.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.