What is the extreme f(x,y)=sqrt(-x^2+1)-sqrt(-y^2+1) ?

The extreme f(x,y)=sqrt(-x^2+1)-sqrt(-y^2+1) 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 f(x,y)=sqrt(-x^2+1)-sqrt(-y^2+1)

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{1}{( y + 1 ) ( y - 1 ) - ( y + 1 ) ( y - 1 )}

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

F (x, y) = 3 x^{2} y - 2 x y^{2} + x + C

f (x) = (2 x)^{x}

\frac{7 z + 6}{z - 7} + \frac{7 z + 3}{z - 7}

f (x) = \frac{( 4 x - 7 )}{x + 3}

\frac{2 x ^{2} - 12 x - 54}{2 x ^{2} + 13 x + 21}

What is the extreme f(x,y)=sqrt(-x^2+1)-sqrt(-y^2+1) ?
The extreme f(x,y)=sqrt(-x^2+1)-sqrt(-y^2+1) is Saddle(0,0)