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

The extreme f(x,y)=x*e^{-(x^2)/2-(y^2)/2} is Minimum(-1,0),Maximum(1,0)

Popular >

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

extreme points

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

Minimum (- 1, 0), Maximum (1, 0)

Solution steps

Find the critical points:

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

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

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

Check the sign of at each critical point

Check critical point

(- 1, 0) :

Minimum

Check critical point

(1, 0) :

Maximum

Minimum (- 1, 0), Maximum (1, 0)

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

f (x) = 2 x^{2} ln (x)

- \frac{1}{3} x^{3} - 5 x^{2} + 2000 x - 326

f (x) = x y (10 - 2 x - 3 y)

y^{3} + 3 x^{2} y - 6 x^{2} - 6 y^{2} + 2

What is the extreme f(x,y)=x*e^{-(x^2)/2-(y^2)/2} ?
The extreme f(x,y)=x*e^{-(x^2)/2-(y^2)/2} is Minimum(-1,0),Maximum(1,0)