Example 4 -- Finding Local Extrema

f = 3x^2 * y + y^3 - 3x^2 - 3y^2 + 2 ;

RowBox[{Plot3D, [, RowBox[{f, ,, {x, -2, 3}, ,, {y, -2, 3}, ,, PlotPoints100, ,, Mesh& ... #62754;, RowBox[{{, RowBox[{.4, ,, RowBox[{-, 2.4}], ,, 1}], }}]}], ,, ClipFillNone}], ]}]

[Graphics:../HTMLFiles/index_51.gif]

RowBox[{RowBox[{ts, =, RowBox[{Join, [, RowBox[{RowBox[{Table, [, RowBox[{RowBox[{{, RowBox[{t ... ,, RowBox[{-, 2.4}], ,, 2, ,, .5}], }}]}], ]}], ,, Table[{2, 2, t}, {t, 1, -1, -.5}]}], ]}]}], ;}]

Do[Plot3D[f, {x, -2, 3}, {y, -2, 3}, PlotRange {-4, 4}, PlotPoints100, ClipFil ... None, MeshFalse, ViewPointts[[t]], TicksNone], {t, 1, Length[ts]}]

[Graphics:../HTMLFiles/index_54.gif]

[Graphics:../HTMLFiles/index_55.gif]

[Graphics:../HTMLFiles/index_56.gif]

[Graphics:../HTMLFiles/index_57.gif]

[Graphics:../HTMLFiles/index_58.gif]

[Graphics:../HTMLFiles/index_59.gif]

[Graphics:../HTMLFiles/index_60.gif]

[Graphics:../HTMLFiles/index_61.gif]

[Graphics:../HTMLFiles/index_62.gif]

[Graphics:../HTMLFiles/index_63.gif]

[Graphics:../HTMLFiles/index_64.gif]

[Graphics:../HTMLFiles/index_65.gif]

[Graphics:../HTMLFiles/index_66.gif]

[Graphics:../HTMLFiles/index_67.gif]

[Graphics:../HTMLFiles/index_68.gif]

[Graphics:../HTMLFiles/index_69.gif]

[Graphics:../HTMLFiles/index_70.gif]

[Graphics:../HTMLFiles/index_71.gif]

ContourPlot[f, {x, -2, 3}, {y, -2, 3}, PlotRange {-4, 4}, ContourShadingFalse, Contours10, PlotPoints100]

[Graphics:../HTMLFiles/index_73.gif]

Created by Mathematica  (December 11, 2003)