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

The extreme f(x,y)=3xy-2x^3y^3 is Saddle(0,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 12 x^{3} y

D (x, y) = - 180 x^{4} y^{4} + 108 x^{2} y^{2} - 9

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

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

- x^{2} - 4 y^{2} + 8 x - 8 y - 16

f (x) = (x - 1)^{2} + y^{2} = 25

f (x) = 2 x^{2} ln (x) - 5 x^{2}

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

What is the extreme f(x,y)=3xy-2x^3y^3 ?
The extreme f(x,y)=3xy-2x^3y^3 is Saddle(0,0)