Let f(x,y)=x3−3xy2f(x, y) = x^3 - 3xy^2f(x,y)=x3−3xy2. Which of the following is true regarding its critical points?
It has exactly one critical point at (0,0)(0, 0)(0,0).
It has infinitely many critical points along the lines y=±13xy = \pm \frac{1}{\sqrt{3}} xy=±31x.
It has no critical points.
The critical point (0,0)(0, 0)(0,0) is a local maximum.