What is the extreme x^3+y^3+9x^2-3y^2+15x-9y ?

The extreme x^3+y^3+9x^2-3y^2+15x-9y is Minimum(-1,3),Saddle(-1,-1),Saddle(-5,3),Maximum(-5,-1)

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extreme x^3+y^3+9x^2-3y^2+15x-9y

extreme points

x^{3} + y^{3} + 9 x^{2} - 3 y^{2} + 15 x - 9 y

Minimum (- 1, 3), Saddle (- 1, - 1), Saddle (- 5, 3), Maximum (- 5, - 1)

Solution steps

Find the critical points:

(- 1, 3), (- 1, - 1), (- 5, 3), (- 5, - 1)

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

D (x, y) = (6 y - 6) (6 x + 18)

Check the sign of at each critical point

Check critical point

(- 1, 3) :

Minimum

Check critical point

(- 1, - 1) :

Saddle

Check critical point

(- 5, 3) :

Saddle

Check critical point

(- 5, - 1) :

Maximum

Minimum (- 1, 3), Saddle (- 1, - 1), Saddle (- 5, 3), Maximum (- 5, - 1)

f (x, y) = e^{1 - y^{2}} - (x^{2} + x y)

\frac{x ^{2} - 2 x + 4}{x - 2}

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

f (x) = 1 - x^{2}, - 1 \leq x \leq 0

f (\frac{x}{y}) = x y + y x

What is the extreme x^3+y^3+9x^2-3y^2+15x-9y ?
The extreme x^3+y^3+9x^2-3y^2+15x-9y is Minimum(-1,3),Saddle(-1,-1),Saddle(-5,3),Maximum(-5,-1)