Find the critical points of the function $f(x,y)=x^{4}+y^{4}-36xy$

Answer :

Starting with the point with the smallest $x$ value, use the Second Derivative Test to determine whether each critical point is

$P_1$
A. a local maximum
B. a local minimum
C. test fails
D. a saddle point
$P_2$
A. a local maximum
B. test fails
C. a saddle point
D. a local minimum
$P_3$
A. a local minimum
B. test fails
C. a saddle point
D. a local maximum