What is the extreme y^2-xy-x^2 ?

The extreme y^2-xy-x^2 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 y^2-xy-x^2

extreme points

y^{2} - x y - x^{2}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (y, x) = - 5

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x, y) = \frac{2 x y ^{2} - x ^{2} y}{x ^{2} + y ^{2}}

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

f (\frac{5}{4}, \frac{1}{4}) = 2 x y - x^{2} - 5 y^{2} + 2 x + 1

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

f (x) = 2 x + 2 y