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

The extreme f(x,y)=x^3+y^3-3x^2-3y^2-9x is Saddle(-1,2),Maximum(-1,0),Minimum(3,2),Saddle(3,0)

Popular >

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

extreme points

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

Saddle (- 1, 2), Maximum (- 1, 0), Minimum (3, 2), Saddle (3, 0)

Solution steps

Find the critical points:

(- 1, 2), (- 1, 0), (3, 2), (3, 0)

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

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

Check the sign of at each critical point

Check critical point

(- 1, 2) :

Saddle

Check critical point

(- 1, 0) :

Maximum

Check critical point

(3, 2) :

Minimum

Check critical point

(3, 0) :

Saddle

Saddle (- 1, 2), Maximum (- 1, 0), Minimum (3, 2), Saddle (3, 0)

f (x) = 2 cos (x) + sin (2 x)

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

f (x) = - x^{2} + 10 x - 21

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

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

What is the extreme f(x,y)=x^3+y^3-3x^2-3y^2-9x ?
The extreme f(x,y)=x^3+y^3-3x^2-3y^2-9x is Saddle(-1,2),Maximum(-1,0),Minimum(3,2),Saddle(3,0)