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Topic: Inflection
Replies: 16   Last Post: Jun 19, 2014 1:07 PM

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Marnie Northington

Posts: 688
Registered: 12/13/04
Re: Inflection
Posted: Jun 18, 2014 3:08 PM
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"Roland Franzius" <roland.franzius@uos.de> wrote in message
news:lnsl57$s9a$1@newsserver.rrzn.uni-hannover.de...
> Am 18.06.2014 19:39, schrieb John Smith:
>> A recent thread about points of inflection reminded me of a function I
>> encountered when I was a math student.
>>
>> The function had many points of inflection but it also had points, which
>> I
>> presume are also called inflection points, where the gradient was
>> infinite
>> (i.e tending to a vertical rather than horizontal line on an x,y graph).
>>
>> I remember the graph looking like a staircase with rounded edges but I
>> have
>> completely forgotten what the function was. It's possible I have not
>> remembered it correctly due to it being so long ago.
>>
>> Can anyone tell me what this function was or give me a similar function?

>
> A candidate is the elliptic integral of the first kind.
>
> F(x,k) = int dphi 1/Sqrt(1-k sin^2 phi)
>
> with k approaching 1 from below.
>
> F represents the physical time as a function of the angle for a rotating
> mathematical pendulum nearly stopping indefinitely long times at the
> sequence of top dead centers phi= (2n+1) pi.
>
> Try
>
> alpha.wolfram.com
>
> plot EllipticF[x,1-10^-14] for 0<x<7pi
>
> Dirct URL
>
> http://www.wolframalpha.com/input/?i=plot+EllipticF[x%2C1-10^-14]+for+0%3Cx%3C7pi


Thanks. It may well have been derived from that. I had to plot a function
y=f(x) myself on graph paper. I think we were going over our answers to the
homework. I remember another student commenting that it had points of
infinite as well as zero gradient.

Old Guy

>
> --
>
> Roland Franzius






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