(* Minima, maxima ans saddle points*)
F=-(E^(-0.05x^2-0.15y^2))
Plot3D[F,{x,-6.,6.},{y,-6.,6.},PlotPoints->15]
ContourPlot[F,{x,-6.,6.},{y,-6.,6.},PlotPoints->60]

x1=x*Cos[Pi/4]+y*Sin[Pi/4]
y1=-x*Sin[Pi/4]+y*Cos[Pi/4]
F=-(E^(-0.05x1^2-0.15y1^2))
Plot3D[F,{x,-6.,6.},{y,-6.,6.},PlotPoints->15]
ContourPlot[F,{x,-6.,6.},{y,-6.,6.},PlotPoints->60]
F=-(E^(-0.05x^2-0.15y^2)) 
Plot3D[F,{x,-6.,6.},{y,-6.,6.},PlotPoints->15]
ContourPlot[F,{x,-6.,6.},{y,-6.,6.},PlotPoints->60]
F=(E^(-0.05x^2-0.15y^2))
Plot3D[F,{x,-6.,6.},{y,-6.,6.},PlotPoints->15]
ContourPlot[F,{x,-6.,6.},{y,-6.,6.},PlotPoints->60]
F=(E^(0.05 x^2-0.15y^2))
Plot3D[F,{x,-5.,5.},{y,-5.,5.},PlotPoints->15]
ContourPlot[F,{x,-5.,5.},{y,-5.,5.},PlotPoints->60]