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

The extreme f(x,y)=(x-y^2)(x-y^3) is Saddle(1,1),Minimum(10/27 , 2/3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

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

Saddle (1, 1), Minimum (\frac{10}{27}, \frac{2}{3})

Solution steps

Find the critical points:

(1, 1), (\frac{10}{27}, \frac{2}{3})

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 (10 y^{3} - 3 x y - x)

D (x, y) = - 9 y^{4} + 28 y^{3} - 4 y^{2} - 12 x y - 4 x

Check the sign of at each critical point

Check critical point

(1, 1) :

Saddle

Check critical point

(\frac{10}{27}, \frac{2}{3}) :

Minimum

Saddle (1, 1), Minimum (\frac{10}{27}, \frac{2}{3})

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

f (x) = 49 x + \frac{16}{x}

f (x) = x^{2} + 10 x + 9

f (x) = x - 2, 0 \leq x \leq 4

y = 7 x - 7 z - 9

What is the extreme f(x,y)=(x-y^2)(x-y^3) ?
The extreme f(x,y)=(x-y^2)(x-y^3) is Saddle(1,1),Minimum(10/27 , 2/3)