Re: unique critical points
- From: "Someonekicked" <someonekicked@xxxxxxxxxxx>
- Date: Fri, 2 Dec 2005 00:39:55 -0500
--
Quotes from The Weather Man:
Robert Spritz: Do you know that the harder thing to do, and the right thing
to do, are usually the same thing? "Easy" doesn't enter into grown-up
life... to get anything of value, you have to sacrifice.
"quasi" <quasi@xxxxxxxx> wrote in message
news:26cvo156vnrmepa22257i5fh7jl4ls77p5@xxxxxxxxxx
> The following result is easy to prove:
>
> Suppose f:R-->R is differentiable. If f has local minimum at x=a and
> no other critical values, then f has a global minimum at x=a.
>
> Next, consider real-valued functions of 2 variables.
>
> Suppose f:R^2-->R is differentiable. If f has local minimum at x=p and
> no other critical points, must f have a global minimum at x=p?
>
> I can see by visualization that the answer to the above question is
> no.
I dont
>
> Can anyone provide a concrete example?
>
> Suppose f is also required to be a polynomial?
>
> quasi
.
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