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From: Ronald Bruck on 29 May 2010 14:42
In article <2tq106daoc9ak9evkk12n9nmm90i1f7vr8(a)4ax.com>, David C.
Ullrich <ullrich(a)math.okstate.edu> wrote:

> On Fri, 28 May 2010 15:14:53 -0700 (PDT), ben <bwcrain(a)gmail.com>
> wrote:
>
> >On May 28, 2:28 pm, W^3 <aderamey.a...(a)comcast.net> wrote:
> >> In article
> >> <ba752028-85d1-46ca-8044-1c4bb7d7d...(a)z17g2000vbd.googlegroups.com>,
> >>
> >>  ben <bwcr...(a)gmail.com> wrote:
> >> > Let x1, x2,...xm be positive variables (actually, >= 1).  The function
> >> > is:
> >>
> >> > 1/(x1*x2*...*xm).
> >>
> >> > Intuitively it's gotta be convex, but I can't prove it. Tried every
> >> > test for convexity I can find, including proof by induction. But they
> >> > become intractable (at least for me).  Any suggestions?
> >>
> >> Assuming the obvious domains, log(1/x) is convex, so each log(1/x_k)
> >> is convex. A sum of convex functions is convex, as is a convex
> >> increasing function of a convex function. Therefore exp(sum
> >> log(1/x_k)) = 1/(x1*x2*...*xm) is convex.
> >
> >Thanx to all my respondents. Makes me feel a bit foolish, now that I
> >see how easy it is, taking logs.
>
> Heh - imagine how _I_ feel. Bad luck that the first thing I thought of
> worked...

At least it wasn't the first thing you thought of in the thread "A
simple proof of FLT" :-)

-- Ron Bruck
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