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

The extreme f(x,y)=(x^2+y^2)e^{-x} is Minimum(0,0),Saddle(2,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

extreme points

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

Minimum (0, 0), Saddle (2, 0)

Solution steps

Find the critical points:

(0, 0), (2, 0)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(2, 0) :

Saddle

Minimum (0, 0), Saddle (2, 0)

3 x^{2} - 18 x + 15

2 x^{3} - 3 x^{2} - 12 x + 18

f (x) = e^{- x^{6}}, - 2 \leq x \leq 1

f (x) = x^{6} - 3 x^{4}

f (x, y) = 4 e^{- 5 x - 5 y}

What is the extreme f(x,y)=(x^2+y^2)e^{-x} ?
The extreme f(x,y)=(x^2+y^2)e^{-x} is Minimum(0,0),Saddle(2,0)