f[x_,y_]:=x^2+y^2
fLinearization[x_,y_]:=2x+2y-2
Manipulate[
GraphicsRow[
{
Plot3D[{f[x,y],fLinearization[x,y]},{x,1-ϵ,1+ϵ},{y,1-ϵ,1+ϵ},PlotRange->{-7,17}],
ContourPlot[f[x,y],{x,1-ϵ,1+ϵ},{y,1-ϵ,1+ϵ},PlotLabel->"f(x,y)"],
ContourPlot[fLinearization[x,y],{x,1-ϵ,1+ϵ},{y,1-ϵ,1+ϵ},PlotLabel->"2x+2y-2"]
}
]
,{ϵ,2,0.001,-0.1}]