I have this function:
$$ f(x,y) = x^2 - 2xy+ 4y^3$$
I calculated the gradient without problems:
$$\nabla f(x,y) = \left(2x-2y , -2x + 12y^3\right)^T$$
This is where kind of got stuck, I know from looking at the gradient that for $(0,0)$ the gradient is $0$, so we have a critical point there but, other than that I'm lost.
I know from $ 2x-2y$ that for for the first part of the gradient to be zero $x$ has to be equal to $y$.
I dont know how to find out the other critical points.