thank you
Remember that $\displaystyle D = \det \begin{bmatrix} f_{xx}&f_{xy} \\ f_{yx}&f_{yy} \end{bmatrix} $.
If $\displaystyle D > 0, \ f_{xx} > 0 $ then we have a minimum. If $\displaystyle D > 0, \ f_{xx} < 0 $ then we have a maximum. If $\displaystyle D < 0 $ then we have a saddle point.
$\displaystyle f_x = 3x^2-3y = 0 $
$\displaystyle f_y = -3y^2-3x = 0 $
Now solve for $\displaystyle (x,y) $ such that the above holds. $\displaystyle (0,0) $ is a critical point. $\displaystyle (-1,1) $ is also CP.