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MathGroup Archive 2005

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Re: Mathematica max, min

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55507] Re: [mg55495] Mathematica max, min
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sun, 27 Mar 2005 02:42:39 -0500 (EST)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

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

(mmpts={x,y,f[x,y]}/.
      Union[Sort/@Solve[Thread[
              (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

> 
> From: diasydias <e at e.com>
To: mathgroup at smc.vnet.net
> Date: 2005/03/26 Sat AM 02:39:25 EST
> To: mathgroup at smc.vnet.net
> Subject: [mg55507] [mg55495] Mathematica max, min
> 
> Hi,
> Could someone pls help me how to input the following max, min problem 
into Mathematica?
> 
> z = 3x^4 + 3x²y -y^3
> 
> Thanks
> 
> 


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