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

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

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

Solution steps

Find the critical points:

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

\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, 0) :

Minimum

Check critical point

(1, 2) :

Saddle

Check critical point

(- 3, 0) :

Saddle

Check critical point

(- 3, 2) :

Maximum

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

\frac{4 x}{x ^{2} - 36}

f (x, y) = x^{3} y^{2} + 5 y^{2} - x + 7

f (x) = x^{3} - 6 x^{2} + 12 x

cos (2 φ)

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

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