Re: Mathematica max, min

• To: mathgroup at smc.vnet.net
• Subject: [mg55583] Re: Mathematica max, min
• From: diasydias <e at e.com>
• Date: Wed, 30 Mar 2005 03:21:30 -0500 (EST)
• References: <d23439\$lgq\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Thank you Bob :-)

Re: Mathematica max, min
Posted: Mar 27, 2005 2:48 AM      Plain Text      Reply

f[x_,y_] := 3*x^4+3*x^2*y-y^3;

(mmpts={x,y,f[x,y]}/.
(D[f[x,y],#]&/@{x,y})==0],
{x,y}]])

{{-(1/2), -(1/2), -(1/16)}, {0, 0, 0}, {1/2, -(1/2), -(1/16)}}

Show[{Plot3D[f[x,y],
{x,-3/4,3/4},{y,-3/4,1/4},
PlotRange->All,
DisplayFunction->Identity],
Graphics3D[{AbsolutePointSize[6],Red,
Point/@mmpts}]},
DisplayFunction->\$DisplayFunction];

It is somewhat easier to see if you zoom-in on each point

Show[{Plot3D[f[x,y],
{x,#[[1]]-0.05,#[[1]]+0.05},
{y,#[[2]]-0.05,#[[2]]+0.05},
PlotRange->All,
DisplayFunction->Identity],
Graphics3D[{AbsolutePointSize[6],Red,
Point[#]}]},
DisplayFunction->\$DisplayFunction]&/@
mmpts;

Bob Hanlon

```

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