What is the extreme f(x)=x^3+y^3+9x^2-9y^2-2 ?

The extreme f(x)=x^3+y^3+9x^2-9y^2-2 is Minimum(0,6),Saddle(0,0),Saddle(-6,6),Maximum(-6,0)

extreme f(x)=x^3+y^3+9x^2-9y^2-2

extreme points

f (x) = x^{3} + y^{3} + 9 x^{2} - 9 y^{2} - 2

Minimum (0, 6), Saddle (0, 0), Saddle (- 6, 6), Maximum (- 6, 0)

Solution steps

Find the critical points:

(0, 6), (0, 0), (- 6, 6), (- 6, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 y - 18

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

Check the sign of at each critical point

Check critical point

(0, 6) :

Minimum

Check critical point

(0, 0) :

Saddle

Check critical point

(- 6, 6) :

Saddle

Check critical point

(- 6, 0) :

Maximum

Minimum (0, 6), Saddle (0, 0), Saddle (- 6, 6), Maximum (- 6, 0)

f (x) = \frac{( x )}{( 6 x + 2 )}, 5 \leq x \leq 8

f (x, y) = (x - 1)^{3} + (x - 1)^{2} + (y + 1)^{2}

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

f (x) = x^{4} - 18 x^{2} + 1, - 6 \leq x \leq 6

f (x) = 3 x^{5} - 25 x^{3} + 60 x

What is the extreme f(x)=x^3+y^3+9x^2-9y^2-2 ?
The extreme f(x)=x^3+y^3+9x^2-9y^2-2 is Minimum(0,6),Saddle(0,0),Saddle(-6,6),Maximum(-6,0)