en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme ye^{x^2-y^2}

Solution

extreme points

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

Solution

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

Solution steps

Find the critical points:

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

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

D (y, x) = 2 y (4 e^{(y + x) (- y + x)} y^{3} - 6 e^{(y + x) (- y + x)} y) (2 e^{x^{2} - y^{2}} x^{2} + e^{x^{2} - y^{2}}) - 4 e^{2 (y + x) (- y + x)} x^{2} (2 y + 1)^{2} (2 y - 1)^{2}

Check the sign of at each critical point

Check critical point

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

Saddle

Check critical point

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

Saddle

Check critical point

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

Saddle

Check critical point

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

Saddle

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

Popular Examples

extreme P(x,y)=3x^2y+4xy^2-y^4 extreme points

P (x, y) = 3 x^{2} y + 4 x y^{2} - y^{4}

extreme f(x)=3x^5-20x^3+16 extreme points

f (x) = 3 x^{5} - 20 x^{3} + 16

extreme (x^3)/(x-2)extreme points

\frac{x ^{3}}{x - 2}

extreme f(x)=sqrt(-x^2+4),-1<= x<= 2 extreme points

f (x) = - x^{2} + 4, - 1 \leq x \leq 2

extreme f(x)=20x^3+9x^2-24x+12,0<= x<= 1 extreme points

f (x) = 20 x^{3} + 9 x^{2} - 24 x + 12, 0 \leq x \leq 1

Frequently Asked Questions (FAQ)

What is the extreme ye^{x^2-y^2} ?
The extreme ye^{x^2-y^2} is