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Re: Mathematica max, min


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]}/.
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


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