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

The extreme f(x,y)=xe^y-x^2-e^y is Saddle(1,ln(2))

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extreme f(x,y)=xe^y-x^2-e^y

extreme points

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

Saddle (1, ln (2))

Solution steps

Find the critical points:

(1, ln (2))

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

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

Check the sign of at each critical point

Check critical point

(1, ln (2)) :

Saddle

Saddle (1, ln (2))

f (x) = \frac{( 5 + x )}{( 3 - x )}

f (x) = - \frac{1}{2} x^{4} + 16 x^{2} - 15

f (x) = 10 x^{\frac{3}{4}} e^{- x}

f (x) = 2 x - 4 y + 6 z = 56

y = 1 - x^{2} - z^{2}

What is the extreme f(x,y)=xe^y-x^2-e^y ?
The extreme f(x,y)=xe^y-x^2-e^y is Saddle(1,ln(2))