What is the extreme f(x,y)=x^3+y^3-243x-27y-2 ?

The extreme f(x,y)=x^3+y^3-243x-27y-2 is Saddle(-9,3),Maximum(-9,-3),Minimum(9,3),Saddle(9,-3)

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extreme f(x,y)=x^3+y^3-243x-27y-2

extreme points

f (x, y) = x^{3} + y^{3} - 243 x - 27 y - 2

Saddle (- 9, 3), Maximum (- 9, - 3), Minimum (9, 3), Saddle (9, - 3)

Solution steps

Find the critical points:

(- 9, 3), (- 9, - 3), (9, 3), (9, - 3)

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

D (x, y) = 36 x y

Check the sign of at each critical point

Check critical point

(- 9, 3) :

Saddle

Check critical point

(- 9, - 3) :

Maximum

Check critical point

(9, 3) :

Minimum

Check critical point

(9, - 3) :

Saddle

Saddle (- 9, 3), Maximum (- 9, - 3), Minimum (9, 3), Saddle (9, - 3)

F (x, y) = 3 y^{2} - 2 y^{2} - 3 x^{2} + 6 x y

\frac{( x - 1 )}{e ^{x + 2}}

14 + 14 x^{- \frac{3}{17}}

f (x, y) = x^{4} + 2 y^{2} - 8 x y

f (x) = x^{4} + y^{3} - 3 \cdot x^{2} + y^{2} + x - 2 \cdot y + 1

What is the extreme f(x,y)=x^3+y^3-243x-27y-2 ?
The extreme f(x,y)=x^3+y^3-243x-27y-2 is Saddle(-9,3),Maximum(-9,-3),Minimum(9,3),Saddle(9,-3)