What is the extreme f(x,y)=xye^{-8y} ?

The extreme f(x,y)=xye^{-8y} is Saddle(0,0)

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extreme f(x,y)=xye^{-8y}

extreme points

f (x, y) = x y e^{- 8 y}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = x (64 e^{- 8 y} y - 16 e^{- 8 y})

D (x, y) = - e^{- 16 y} (- 8 y + 1)^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x, y) = x^{2} - x y + y^{2} + 4 x + 7 y

x^{3} + y^{3} - 6 y^{2} - 3 x + 9

\frac{2 x ^{2}}{( x + 1 ) ^{2}}

f (x) = x^{2} - 4 x - 6

What is the extreme f(x,y)=xye^{-8y} ?
The extreme f(x,y)=xye^{-8y} is Saddle(0,0)