h[x_,y_]=x*Exp[-((x^2)+(y^2))];

eqn1=D[h[x,y],x]==0
sol1=Solve[eqn1,x]
eqn2=D[h[x,y],y]==0
sol2=Solve[eqn2,y]

FindMaximum[h[x,y],{x,y}]

FindMinimum[h[x,y],{x,-1},{y,0}]

Plot3D[{h[x,y]},{x,-2,2},{y,-2,2},AxesLabel->{x,y,z}]