What is the extreme f(x,y)=7-x^4+2x^2-y^2 ?

The extreme f(x,y)=7-x^4+2x^2-y^2 is Saddle(0,0),Maximum(-1,0),Maximum(1,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x,y)=7-x^4+2x^2-y^2

extreme points

f (x, y) = 7 - x^{4} + 2 x^{2} - y^{2}

Saddle (0, 0), Maximum (- 1, 0), Maximum (1, 0)

Solution steps

Find the critical points:

(0, 0), (- 1, 0), (1, 0)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(- 1, 0) :

Maximum

Check critical point

(1, 0) :

Maximum

Saddle (0, 0), Maximum (- 1, 0), Maximum (1, 0)

x + 1

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

\frac{3 x - 6}{x + 2}

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

f (x) = 4 sin (x) + 4 cos (x)

What is the extreme f(x,y)=7-x^4+2x^2-y^2 ?
The extreme f(x,y)=7-x^4+2x^2-y^2 is Saddle(0,0),Maximum(-1,0),Maximum(1,0)