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

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

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

extreme points

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

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

Solution steps

Find the critical points:

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

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

D (x, y) = - 72 x y

Check the sign of at each critical point

Check critical point

(- 2, 3) :

Maximum

Check critical point

(- 2, - 3) :

Saddle

Check critical point

(2, 3) :

Saddle

Check critical point

(2, - 3) :

Minimum

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

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