What is the extreme f(x,y)=x^3+y^3-108x-27y-6 ?

The extreme f(x,y)=x^3+y^3-108x-27y-6 is Saddle(-6,3),Maximum(-6,-3),Minimum(6,3),Saddle(6,-3)

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extreme f(x,y)=x^3+y^3-108x-27y-6

extreme points

f (x, y) = x^{3} + y^{3} - 108 x - 27 y - 6

Saddle (- 6, 3), Maximum (- 6, - 3), Minimum (6, 3), Saddle (6, - 3)

Solution steps

Find the critical points:

(- 6, 3), (- 6, - 3), (6, 3), (6, - 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

(- 6, 3) :

Saddle

Check critical point

(- 6, - 3) :

Maximum

Check critical point

(6, 3) :

Minimum

Check critical point

(6, - 3) :

Saddle

Saddle (- 6, 3), Maximum (- 6, - 3), Minimum (6, 3), Saddle (6, - 3)

f (x) = x^{4} + x^{3} - 3 x^{2} - 5 x - 2

f (x) = cos (π x), 0 \leq x \leq \frac{1}{6}

f (x) = - 2 x^{3} + 12 x

f (x, y) = 6 e^{- 2 x - 2 y}

f (x) = 45 - 3 x

What is the extreme f(x,y)=x^3+y^3-108x-27y-6 ?
The extreme f(x,y)=x^3+y^3-108x-27y-6 is Saddle(-6,3),Maximum(-6,-3),Minimum(6,3),Saddle(6,-3)