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

The extreme f(x,y)=y^3-x^3-3xy is Saddle(0,0),Maximum(1,-1)

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extreme f(x,y)=y^3-x^3-3xy

extreme

Saddle (0, 0), Maximum (1, - 1)

Solution steps

Find the critical points:

(0, 0), (1, - 1)

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

D (x, y) = - 36 x y - 9

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(1, - 1) :

Maximum

Saddle (0, 0), Maximum (1, - 1)

What is the extreme f(x,y)=y^3-x^3-3xy ?
The extreme f(x,y)=y^3-x^3-3xy is Saddle(0,0),Maximum(1,-1)