Example 1 -- Local and Absolute Extrema

The function g in this example has local maxima at (2,3) and (-2,-1), local minima at (-2,3) and (2,-1), an absolute maximum at (2,3), and an absolute minimum at (-2,3).

g = 3/(1 + (-2 + x)^2 + (-3 + y)^2)^2 - 3/(1 + (2 + x)^2 + (-3 + y)^2)^2 - 1/(1 + (-2 + x)^2 + y^2)^2 + 1/(1 + (2 + x)^2 + y^2)^2 ;

Plot3D[g, {x, -5, 5}, {y, -2, 5}, PlotPoints45, PlotRange {-3, 3}, MeshFalse, ViewPoint {0, -2, 2}, AxesLabel {x, y, z}]

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

Do[Plot3D[g, {x, -5, 5}, {y, -2, 5}, PlotPoints45, PlotRange {-3, 3}, MeshFalse, ViewPoint {0, -2, -ts[[t]]}, TicksNone], {t, 1, Length[ts]}]

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ContourPlot[g, {x, -5, 5}, {y, -2, 5}, ContourShadingFalse, Contours20, PlotPoints45]

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Created by Mathematica  (December 11, 2003)