What is the extreme f(x)=16xy-x^3-8y^2 ?

The extreme f(x)=16xy-x^3-8y^2 is Saddle(0,0),Maximum(16/3 , 16/3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=16xy-x^3-8y^2

extreme points

f (x) = 16 x y - x^{3} - 8 y^{2}

Saddle (0, 0), Maximum (\frac{16}{3}, \frac{16}{3})

Solution steps

Find the critical points:

(0, 0), (\frac{16}{3}, \frac{16}{3})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 16

D (x, y) = 96 x - 256

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(\frac{16}{3}, \frac{16}{3}) :

Maximum

Saddle (0, 0), Maximum (\frac{16}{3}, \frac{16}{3})

What is the extreme f(x)=16xy-x^3-8y^2 ?
The extreme f(x)=16xy-x^3-8y^2 is Saddle(0,0),Maximum(16/3 , 16/3)