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


Gerry Myerson wrote:
>
> [...]
>
> So I think the bottom line is,
>
> 1) if you're a student in a calculus class, a point of
> inflection is whatever your teacher says it is, and
>
> 2) if you're not a student in a calculus class, and for
> some reason you feel compelled to make use of the
> concept of a point of inflection, be sure you spell
> out exactly what you mean by it.

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.

.