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

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Marnie Northington

Posts: 1,251
Registered: 12/13/04
Re: Inflection
Posted: Jun 19, 2014 1:07 PM
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"Port563" <> wrote in message
> "John Smith" <invalid@invalid.invalid> wrote...

>> "quasi" <quasi@null.set> wrote in message

>>> John Smith wrote:
>>>>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?

>>> The curve given by the implicit equation
>>> x - y = sin(x + y)
>>> has the shape you described.

>> Thanks, that looks very like what I remember but I can't remember whether
>> it was horizontal or vertical at the origin.

> Or neither?
> Take a look at
> x - y = 1 - cos(x + y)
> and tell me where you want your stairs shifted to. (-:

Ok I guess we can put the origin anywhere.
I remember a math(s) lecturer telling us all about that.

But whatever I plotted I'm fairly sure it would have been in the form y =
f(x) in closed form and I don't think the above function can be put in that

Old Guy

> Before the village idiot joins in, the slope at the origin is 1.

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