What is the extreme f(x,y)=x(e^x-e^y) ?

The extreme f(x,y)=x(e^x-e^y) is Saddle(0,0)

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extreme f(x,y)=x(e^x-e^y)

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 9 x^{2} - 27 x + 6

f (x) = 2 x^{3} - 24 x + 6

f (x) = \frac{16 ( x + 3 )}{x ^{4}}

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

w^{4} - 55 w^{2} + 1600

What is the extreme f(x,y)=x(e^x-e^y) ?
The extreme f(x,y)=x(e^x-e^y) is Saddle(0,0)