Re: Re: Local extrema of a function of two variables

• To: mathgroup at smc.vnet.net
• Subject: [mg90035] Re: [mg90017] Re: Local extrema of a function of two variables
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Fri, 27 Jun 2008 06:14:19 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200806260844.EAA21022@smc.vnet.net>
• Reply-to: murray at math.umass.edu

```That's nice: I didn't know about the "trick" of getting the entire
Hessian matrix in one simple expression D[f[x, y], {{x, y}, 2}],
although of course it's documented at tutorial/Differentiation.

It's interesting that Mathematica (at least version 6) includes a System
symbol Hessian...

?Hessian
System`Hessian
Attributes[Hessian] = {Protected}

...but apparently no associated definition and no reference page in the
Documentation Center.

Jean-Marc Gulliet wrote:
>
> ...Now,we compute the Hessian matrix, *)
>
> hessian = D[f[x, y], {{x, y}, 2}]
>
> {{-12 x^2, 4}, {4, -12 y^2}}
>
> (* and take its determinant: *)
>
> d = hessian // Det
>
> -16 + 144 x^2 y^2
> ...
--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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