What is the extreme f(x,y)=4xy-x^2y-xy^2 ?

The extreme f(x,y)=4xy-x^2y-xy^2 is Saddle(0,4),Maximum(4/3 , 4/3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x,y)=4xy-x^2y-xy^2

extreme points

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

Saddle (0, 4), Maximum (\frac{4}{3}, \frac{4}{3})

Solution steps

Find the critical points:

(0, 4), (\frac{4}{3}, \frac{4}{3})

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

D (x, y) = - 4 x y + 16 x - 4 x^{2} + 16 y - 4 y^{2} - 16

Check the sign of at each critical point

Check critical point

(0, 4) :

Saddle

Check critical point

(\frac{4}{3}, \frac{4}{3}) :

Maximum

Saddle (0, 4), Maximum (\frac{4}{3}, \frac{4}{3})

f (x) = \frac{1}{4} x^{4} - 2 x^{2}

f (x) = x^{3} (x - 5)^{2}

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

f (x) = \frac{1}{4} x + 3 + \frac{400}{x}

f (x) = cos (x) - x

What is the extreme f(x,y)=4xy-x^2y-xy^2 ?
The extreme f(x,y)=4xy-x^2y-xy^2 is Saddle(0,4),Maximum(4/3 , 4/3)