What is the extreme f(x)=ye^{(x^2-y^2)} ?

The extreme f(x)=ye^{(x^2-y^2)} is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=ye^{(x^2-y^2)}

extreme points

f (x) = y e^{(x^{2} - y^{2})}

Saddle (0, - \frac{1}{2}), Saddle (0, \frac{1}{2}), Saddle (0, - \frac{1}{2}), Saddle (0, \frac{1}{2})

Solution steps

Find the critical points:

(0, - \frac{1}{2}), (0, \frac{1}{2}), (0, - \frac{1}{2}), (0, \frac{1}{2})

\frac{\partial ^{2} f}{\partial x ^{2}} = 4 e^{(x + y) (x - y)} y^{3} - 6 e^{(x + y) (x - y)} y

D (x, y) = 16 e^{2 x^{2} - 2 y^{2}} x^{2} y^{4} - 16 e^{2 (x^{2} - y^{2})} x^{2} y^{4} + 8 e^{2 x^{2} - 2 y^{2}} y^{4} - 8 e^{2 x^{2} - 2 y^{2}} x^{2} y^{2} - 12 e^{2 x^{2} - 2 y^{2}} y^{2} - 4 e^{2 (x^{2} - y^{2})} x^{2}

Check the sign of at each critical point

Check critical point

(0, - \frac{1}{2}) :

Saddle

Check critical point

(0, \frac{1}{2}) :

Saddle

Check critical point

(0, - \frac{1}{2}) :

Saddle

Check critical point

(0, \frac{1}{2}) :

Saddle

Saddle (0, - \frac{1}{2}), Saddle (0, \frac{1}{2}), Saddle (0, - \frac{1}{2}), Saddle (0, \frac{1}{2})

f (x) = 8 x + 6 y - 1 = 0

10 x e^{- 2 x}

f (x) = \frac{e ^{x}}{x ^{3}}, x > 0

f (x, y) = ln (y - ∣ x ∣ - 1)

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