Re: RE: [Math4u] Re: Maxima & Minima

First of, sorry for the weird characters in my last
post, here it is again, this time I double-checked
everything is normal characters:

> > http://en.wikipedia.org/wiki/Maxima_and_minima
> > [A] function has a local minimum point at x'
> > if f(x') <= f(x) when |x < x'| < epsilon
> > -> Note the use of smaller-or-equal (instead of
> > strictly smaller)

Second, Sanjiva, here is your original definition
again (slightly reformatted), just to refresh the
memory of everyone reading this thread:

> > > The statement of my question is proved false
> > > by the following example:
> > > f(x) = sin x, x <= 3*pi/2
> > > = -1, 3*pi/2 < x < 7*pi/2
> > > = sin x, 7*pi/2 <= x

If Brian says

> > > max at (pi/2,1)
> > > min at (3pi/2,-1)
> > > max at (5pi/2,1)
> > > min at (7pi/2, -1)
> > > max at 9pi/2,1)

then replying "there is no minima at 3pi/2 and 7pi/2"
is at least confusing; how about "I do not agree the
points 3pi/2 and 7pi/2 are minima (and there is most
definitely no maximum at 5pi/2; I think you haven't
understood my function definition correctly)."?

And finally, if Mathworld and Wikipedia say "yes" (or
"<=" for that matter) and you say "no" (or "<"), then
you better give a pretty good reason for that. If you
just claim it, without so much as giving a reason, I
for one will simply consider you wrong.
Think about it this way, if I said "1 > 2", without
any reasoning whatsoever, you wouldn't take my word
for it either, would you?

Grtz,
Rob

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