What is the extreme f(x,y)=18y^2+x^2-x^2y ?

The extreme f(x,y)=18y^2+x^2-x^2y is Minimum(0,0),Saddle(6,1),Saddle(-6,1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x,y)=18y^2+x^2-x^2y

extreme points

f (x, y) = 18 y^{2} + x^{2} - x^{2} y

Minimum (0, 0), Saddle (6, 1), Saddle (- 6, 1)

Solution steps

Find the critical points:

(0, 0), (6, 1), (- 6, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 36

D (x, y) = 36 (2 - 2 y) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(6, 1) :

Saddle

Check critical point

(- 6, 1) :

Saddle

Minimum (0, 0), Saddle (6, 1), Saddle (- 6, 1)

2 x^{3} + 2 y^{3} - 9 x^{2} + 3 y^{2} - 12 y

f (x, y) = 2 x + x y + 2 y

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

f (x) = x^{2} + y^{2} + 6 x - 18 y

f (x) = (x - 9)^{2}

What is the extreme f(x,y)=18y^2+x^2-x^2y ?
The extreme f(x,y)=18y^2+x^2-x^2y is Minimum(0,0),Saddle(6,1),Saddle(-6,1)