# Re: How find the max value of the one 3D function in a interval?

• To: mathgroup@smc.vnet.net
• Subject: [mg11849] Re: How find the max value of the one 3D function in a interval?
• From: Bill Bertram <wkb@ansto.gov.au>
• Date: Wed, 1 Apr 1998 00:35:53 -0500
• Organization: ANSTO
• References: <6fq2vf\$cre@smc.vnet.net>

```Fernando Marcos Santana Barreto wrote:
>
> I have one function
>
> w[x_,y_] := Sin[x]*Cos[y];
>
> and I need to get the max value of the function in a determinate
> interval
>
> for example
>
> {x,0,1},{y,-1,0}
> How can I do that?

You could try the package "MultiplierMethod" obtainable from Mathsource/
Applications/mathematics/0207-289.

This uses the Lagrangian method of multipliers to solve constrained
minimization problems. By applying this method to the INVERSE of your
function it will hopefully give you its local maximum.

For the example you have given, this works ie.

w[x_,y_]:= Sin[x]Sin[y] ;
MultiplierMethod[1/w[x,y],{ },{-x, x-Pi,-y, y-Pi},{x,y},{1.,1.}]

gives the local maximum in the interval {{0,Pi},{0,Pi}} as

{1.,{x->1.5708,y->1.5708}}

Hope this helps,
Bill

```

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