Re: true or false: (x^5 - x) has inflexion point at origin, (x^4 - x) doesn't
- From: "Proginoskes" <CCHeckman@xxxxxxxxx>
- Date: 25 Aug 2005 18:50:14 -0700
john_ramsden@xxxxxxxxxxxxxx wrote:
> Robert Israel wrote:
> > In article <1124960183.220303.114120@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> > <john_ramsden@xxxxxxxxxxxxxx> wrote:
> >
> > >I've always presumed that an inflection of y = y(x) is a
> > >point where y'' = 0, whether this is an extrema of y' or
> > >only a turning point (which is apparently the distinction
> > >some definitions are intended to make).
> >
> > >But obviously opinion is still divided, which for a concept
> > >so basic and long-established is astonishing.
> >
> > I'm not aware of any published source that agrees with your
> > definition. To come back to the Subject line, nobody would
> > say that x^4 - x has an inflection at x=0.
> >
> > Robert Israel israel@xxxxxxxxxxx
> > Department of Mathematics http://www.math.ubc.ca/~israel
> > University of British Columbia Vancouver, BC, Canada
>
> It does seem like I was plain wrong to think an inflection
> of y = y(x) was synonymous with a point satisfying y'' = 0.
> (Wikipedia says the first implies the second, but that the
> converse need not hold.)
The places where y'' = 0 are more like critical points in nature, but
they're (formally) critical points of y'. That's the closest I've seen
to a name given to places where y'' = 0. (Last semester, I had a
discussion similar to this one with one of the instructors at ASU, but
with y = x^4.)
--- Christopher Heckman
.
- References:
- true or false: (x^5 - x) has inflexion point at origin, (x^4 - x) doesn't
- From: David Jones
- Re: true or false: (x^5 - x) has inflexion point at origin, (x^4 - x) doesn't
- From: Robert Israel
- Re: true or false: (x^5 - x) has inflexion point at origin, (x^4 - x) doesn't
- From: Gerry Myerson
- Re: true or false: (x^5 - x) has inflexion point at origin, (x^4 - x) doesn't
- From: john_ramsden
- Re: true or false: (x^5 - x) has inflexion point at origin, (x^4 - x) doesn't
- From: Robert Israel
- Re: true or false: (x^5 - x) has inflexion point at origin, (x^4 - x) doesn't
- From: john_ramsden
- true or false: (x^5 - x) has inflexion point at origin, (x^4 - x) doesn't
- Prev by Date: Re: how to solve this equation by paper and pencil?
- Next by Date: Re: what is the number ?
- Previous by thread: Re: true or false: (x^5 - x) has inflexion point at origin, (x^4 - x) doesn't
- Next by thread: Re: true or false: (x^5 - x) has inflexion point at origin, (x^4 - x) doesn't
- Index(es):
Relevant Pages
|
