<sagecell> var('x,y') #Name your variables
f(x,y)=x^2+4*x*y-4*x+6*y+y^2
gradf=f.diff() gradf
sol=solve([gradf()[0]==0,gradf()[1]==0],(x,y)) show(sol)
p=plot_vector_field(gradf,(x,-14/3,-2/3),(y,1/3,13/3))
p+=implicit_plot(f==f(-8/3,7/3),(x,-14/3,-2/3),(y,1/3,13/3)) p+=contour_plot(f,(x,-14/3,-2/3),(y,1/3,13/3),fill=false,contours=27)
show(p) </sagecell>