f[x_,y_]=3 x^2+12 x+4 y^3-6 y^2+5;

graf=ContourPlot3D[z==f[x,y]  ,{x,-4,0},{y,-1,2},{z,-20,15},ContourStyle->{Opacity[0.3],LightGray}]

Grad[f[x,y],{x,y}]

Solve[%=={0,0}]

{f[-2,0],f[-2,1]}

graf2=Show[graf,Graphics3D[{PointSize[Large],Blue,Thick,Point[{{-2,0,-7},{-2,1,-9}}]}]]

plano1=Plot3D[-7,{x,-2.4,-1.6},{y,-0.4,0.4},Mesh->False,PlotStyle->{Opacity[0.3],LightRed},BoundaryStyle->{Blue,Thick}];

plano2=Plot3D[-9,{x,-2.4,-1.6},{y,0.6,1.4},Mesh->False,PlotStyle->{Opacity[0.3],LightRed},BoundaryStyle->{Blue,Thick}];

Show[graf2,plano1,plano2]