f  =  2  (x^3) - 6  x*y - 3  (y^2)

fx  =  D[f, x]

fy  =  D[f, y]

fxx = D[fx, x]

fyy = D[fy, y]

fxy = D[fx, y]

Der  = (fxx) (fyy) - (((fxy))^2)

Solve[{fx == 0, fy == 0}, {x, y}]

Function[{x, y}, -36 - 72  x][0, 0]

Function[{x, y}, -36 - 72  x][-1, 1]

\(ContourPlot[f, {x, \(-2\), 1}, {y, \(-1\), 2}, Axes -> True, \ 
      AxesLabel -> {"x-direction", "y-direction"}, \ 
Contours -> 50, \ 
      ContourShading -> False]\)

\(Plot3D[f, {x, \(-2\), 1}, {y, \(-1\), 2}, \ 
      BoxRatios -> {1, 1, 1}, 
Axes -> True, \ 
      AxesLabel -> {"x-direction", "y-direction", \ "z-direction"}]\)