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?
Best Answer
HINT
We have that for $f(x,y)=x^3+y^4-6x-2y^2$
then evaluate
at each critical point and consider the Hessian determinant at each point.
Refer to