What is the extreme x^3+y^3-27x-48y-24 ?

The extreme x^3+y^3-27x-48y-24 is Saddle(-3,4),Maximum(-3,-4),Minimum(3,4),Saddle(3,-4)

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extreme x^3+y^3-27x-48y-24

extreme points

x^{3} + y^{3} - 27 x - 48 y - 24

Saddle (- 3, 4), Maximum (- 3, - 4), Minimum (3, 4), Saddle (3, - 4)

Solution steps

Find the critical points:

(- 3, 4), (- 3, - 4), (3, 4), (3, - 4)

\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

(- 3, 4) :

Saddle

Check critical point

(- 3, - 4) :

Maximum

Check critical point

(3, 4) :

Minimum

Check critical point

(3, - 4) :

Saddle

Saddle (- 3, 4), Maximum (- 3, - 4), Minimum (3, 4), Saddle (3, - 4)

f (x) = e^{- x} \cdot (x^{2} - x + 1)

f (x) = - 2 x^{2} + 60 x - 70

y = \frac{cos ( x )}{1 + sin ^{2} ( x )}

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

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

What is the extreme x^3+y^3-27x-48y-24 ?
The extreme x^3+y^3-27x-48y-24 is Saddle(-3,4),Maximum(-3,-4),Minimum(3,4),Saddle(3,-4)