Re: true or false: (x^5 - x) has inflexion point at origin, (x^4 - x) doesn't

In article <dektvj$sp0$1@xxxxxxxxxxxxxxxxxxxxxx>,
israel@xxxxxxxxxxx (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.

Not so.
http://www.maths.mq.edu.au/~wchen/lnfycfolder/fyc05-d.pdf
is Chapter 5 of the notes we use to teach 1st-year math
at Macquarie University. On page 7 it says,

Definition. We say that a function f(x) has a point of inflection
at x = a if f''(a) = 0.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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