Second derivative test for discriminant Question: Find all critical points of $f(x,y)=x^3+y^4-6x-2y^2$
Apply 2nd Derivative test to each point and determine whether it is local maximum, local minimum or saddle point or that the test fails.
I have found six critical points in total and applying the discriminant equation for 2 variables [ discriminant= (fxx)(fyy) - (fxy)^2 , which is 24x(3y^2 -1) in this question ] , what should be my next step?

HINT
We have that for $f(x,y)=x^3+y^4-6x-2y^2$


*

*$f_x=3x^2-6=0 \implies x=\pm \sqrt 2$

*$f_y=4y^3-4y=0 \implies y=0 \,\lor\,y=\pm 1$
then evaluate


*

*$f_{xx}=6x$

*$f_{xy}=f_{yx}=0$

*$f_{yy}=12y^2-4$
at each critical point and consider the Hessian determinant at each point.
Refer to 


*

*Second partial derivative test
