What is the extreme x^3+3xy^2-39x-36y+36 ?

The extreme x^3+3xy^2-39x-36y+36 is Saddle(2,3),Saddle(-2,-3),Minimum(3,2),Maximum(-3,-2)

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extreme x^3+3xy^2-39x-36y+36

extreme points

x^{3} + 3 x y^{2} - 39 x - 36 y + 36

Saddle (2, 3), Saddle (- 2, - 3), Minimum (3, 2), Maximum (- 3, - 2)

Solution steps

Find the critical points:

(2, 3), (- 2, - 3), (3, 2), (- 3, - 2)

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

D (x, y) = 36 x^{2} - 36 y^{2}

Check the sign of at each critical point

Check critical point

(2, 3) :

Saddle

Check critical point

(- 2, - 3) :

Saddle

Check critical point

(3, 2) :

Minimum

Check critical point

(- 3, - 2) :

Maximum

Saddle (2, 3), Saddle (- 2, - 3), Minimum (3, 2), Maximum (- 3, - 2)

What is the extreme x^3+3xy^2-39x-36y+36 ?
The extreme x^3+3xy^2-39x-36y+36 is Saddle(2,3),Saddle(-2,-3),Minimum(3,2),Maximum(-3,-2)