Example 2 -- Local and Absolute Extrema

The function g in this example has no local or absolute extrema.  It does, however, have a saddle point at (0,0).

g = y^2 - x^2 ;

Plot3D[g, {x, -4, 4}, {y, -4, 4}, PlotPoints15, PlotRange {-16, 16}, MeshTrue, AxesLabel {x, y, z}]

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ts = Table[t, {t, -2, 2, .5}] ;

RowBox[{Do, [, RowBox[{RowBox[{Plot3D, [, RowBox[{g, ,, {x, -4, 4}, ,, {y, -4, 4}, ,, PlotPoin ... RowBox[{-, 2.4}], ,, -ts[[t]]}], }}]}], ,, TicksNone}], ]}], ,, {t, 1, Length[ts]}}], ]}]

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ContourPlot[g, {x, -4, 4}, {y, -4, 4}, ContourShadingFalse, Contours20, PlotPoints15]

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Created by Mathematica  (December 11, 2003)