Find all critical points of f(x,y)=x3+y3−3xyf(x, y) = x^3 + y^3 - 3xyf(x,y)=x3+y3−3xy and classify the critical point(s).
(0,0)(0, 0)(0,0) is a saddle point; (1,1)(1, 1)(1,1) is a local minimum
(1,1)(1, 1)(1,1) is a saddle point; (0,0)(0, 0)(0,0) is a local minimum
(0,0)(0, 0)(0,0) is a local maximum; (1,1)(1, 1)(1,1) is a saddle point
(0,0)(0, 0)(0,0) and (1,1)(1, 1)(1,1) are both saddle points