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

The extreme f(x,y)=x^2+y-e^{x+y} is Saddle(1/2 ,-1/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

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

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

Solution steps

Find the critical points:

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

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

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

Check the sign of at each critical point

Check critical point

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

Saddle

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

f (x) = x^{3} + y^{2} - 6 x^{2} + y - 1

- x

f (x) = \frac{3 x}{x + 2}

f (x) = 6 x + 4 y + 2 z = 24

f (x, y) = \frac{16}{x} + \frac{6}{y} + x^{2} - 3 y^{2}

What is the extreme f(x,y)=x^2+y-e^{x+y} ?
The extreme f(x,y)=x^2+y-e^{x+y} is Saddle(1/2 ,-1/2)