Only Critical Point in Town Test

Author

Eric W. Weisstein
April 14, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/OnlyCriticalPointinTownTest.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/OnlyCriticalPointinTownTest.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Plots

Show[GraphicsArray[{Plot3D[3x Exp[y]-x^3-Exp[3y],{x,-2,2},{y,-2,2},PlotRange->{-30,5},ViewPoint->{2,2,2},ClipFill->None,DisplayFunction->Identity],
Plot3D[x^2(1+y)^3+y^2,{x,-2,2},{y,-2,2},PlotRange->{-2,10},ViewPoint->{2,2,2},ClipFill->None,DisplayFunction->Identity]
Plot3D[x y(x^2-y^2)/(x^2+y^2),{x,-2,2},{y,-2,2},DisplayFunction->Identity,ViewPoint->{2,2,2},ClipFill->None]}],
DisplayFunction->$DisplayFunction]

LiveGraphics3D

<<Utilities`LiveGraphics3D`

WriteLiveForm["onlycr1.m",ClipAtPlotRange[Plot3D[3x Exp[y]-x^3-Exp[3y],{x,-2,2},{y,-2,2},PlotRange->{-30,5},ViewPoint->{2,2,2},ClipFill->None]]]

WriteLiveForm["onlycr2.m",
	ClipAtPlotRange[
	Plot3D[x^2(1+y)^3+y^2,{x,-2,2},{y,-2,2},
PlotRange->{-2,10},ViewPoint->{2,2,2},
	ClipFill->None,
		LightSources->{{{1.,0.,1.},RGBColor[1,0,0]},
	{{1.,1.,1.},RGBColor[0,1,0]},
	{{0.,1.,1.},RGBColor[0,0,1]},
	{{-1.,-1.,-1.},RGBColor[.5,.5,.5]}}]]]