Plot3D[x^2*y(2-x-y),{x,-3,3},{y,-3,3}]

a=Plot3D[x^2*y(2-x-y),
{x,-3,3},(* x-range *)
{y,-3,3},(* y-range *)
PlotRange->{-1,0.5},(* z-range *)
PlotPoints->150 (*snyggare slätare kurva*)
]

Vi tittar på kurvan y=1:

Plot[x^2*(1-x),{x,-2,2},PlotRange->{-0.5,2}]

ContourPlot[x^2*y*(2-x-y),
{x,-3,3},
{y,-3,3},
Contours->{-2,-1,-0.5,0,0.1,0.2,0.3,0.5,1},
ContourShading->None
]

b=ListPointPlot3D[{{0,0,0},{0,2,0}},PlotStyle->{Black,PointSize[0.02]}]

c=Plot3D[x^2*y(2-x-y),
{x,-3,3},
{y,-3,3},
PlotRange->{-1,0.5},
PlotPoints->150,
MeshFunctions->{#3&}
]

d=ParametricPlot3D[{0,t,0},{t,-3,3},PlotStyle->Directive[Black,Thick]]

Show[c,d]

e=ListPointPlot3D[{{0,0,0},{0,2,0}},
PlotStyle->{Black,PointSize[0.02]}(* punkterna ska vara svart med en storlek som är lagom till figuren*)
]

f=ListPointPlot3D[{{2,0,0}},PlotStyle->{Blue,PointSize[0.02]}]

g=ListPointPlot3D[{{1,1/2,1/4}},PlotStyle->{Red,PointSize[0.02]}]

Show[c,d,e,f,g]

Show[a,c,d,e,f,g]