What is the FUNCTION_MANY#extreme f(x,y)=x^3+y^3-33xy ?

The FUNCTION_MANY#extreme f(x,y)=x^3+y^3-33xy is Saddle(0,0),Minimum(11,11)

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FUNCTION_MANY#extreme f(x,y)=x^3+y^3-33xy

extreme points

f (x, y) = x^{3} + y^{3} - 33 x y

Saddle (0, 0), Minimum (11, 11)

Solution steps

Find the critical points:

(0, 0), (11, 11)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 y

D (x, y) = 36 x y - 1089

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(11, 11) :

Minimum

Saddle (0, 0), Minimum (11, 11)

What is the FUNCTION_MANY#extreme f(x,y)=x^3+y^3-33xy ?
The FUNCTION_MANY#extreme f(x,y)=x^3+y^3-33xy is Saddle(0,0),Minimum(11,11)