What is the extreme f(x,y)=-x^3+2y^3+27x-24y+3 ?

The extreme f(x,y)=-x^3+2y^3+27x-24y+3 is Minimum(-3,2),Saddle(-3,-2),Saddle(3,2),Maximum(3,-2)

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extreme f(x,y)=-x^3+2y^3+27x-24y+3

extreme points

f (x, y) = - x^{3} + 2 y^{3} + 27 x - 24 y + 3

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

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = 12 y

D (x, y) = - 72 x y

Check the sign of at each critical point

Check critical point

(- 3, 2) :

Minimum

Check critical point

(- 3, - 2) :

Saddle

Check critical point

(3, 2) :

Saddle

Check critical point

(3, - 2) :

Maximum

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

f (x) = \frac{x ^{2}}{e ^{x}}

F (I, J) = (- 3 I + 2 J)

f (x) = x_{1} x

0.5 x^{2} - 130 x + 17555

f (x, y) = x - y - x^{2} y + x y^{2}

What is the extreme f(x,y)=-x^3+2y^3+27x-24y+3 ?
The extreme f(x,y)=-x^3+2y^3+27x-24y+3 is Minimum(-3,2),Saddle(-3,-2),Saddle(3,2),Maximum(3,-2)