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Re: Inflection
Posted:
Jun 19, 2014 1:07 PM


"Port563" <reader80@eternalseptember.org> wrote in message news:lnv42u$d6e$1@dontemail.me... > > "John Smith" <invalid@invalid.invalid> wrote... >> "quasi" <quasi@null.set> wrote in message >> news:v325q9difmb8tvcerh2askpo48dnn8vv0j@4ax.com... >>> 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 form.
Old Guy
> > Before the village idiot joins in, the slope at the origin is 1. >



