What is the extreme f(x,y)=xy+ln(x)+32y^2 ?

The extreme f(x,y)=xy+ln(x)+32y^2 is Saddle(-8, 1/8),Saddle(8,-1/8)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x,y)=xy+ln(x)+32y^2

extreme points

f (x, y) = x y + ln (x) + 32 y^{2}

Saddle (- 8, \frac{1}{8}), Saddle (8, - \frac{1}{8})

Solution steps

Find the critical points:

(- 8, \frac{1}{8}), (8, - \frac{1}{8})

\frac{\partial ^{2} f}{\partial x ^{2}} = 64

D (x, y) = - \frac{64}{x ^{2}} - 1

Check the sign of at each critical point

Check critical point

(- 8, \frac{1}{8}) :

Saddle

Check critical point

(8, - \frac{1}{8}) :

Saddle

Saddle (- 8, \frac{1}{8}), Saddle (8, - \frac{1}{8})

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

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

f (x, y) = 2 x y

x^{4} ln (x)

f (x) = x^{4} - 18 x^{2} + 1

What is the extreme f(x,y)=xy+ln(x)+32y^2 ?
The extreme f(x,y)=xy+ln(x)+32y^2 is Saddle(-8, 1/8),Saddle(8,-1/8)