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{4 x + 6}{x + 2}

f (x) = (3000 x - 2 x^{2})

f (x) = 4 x^{\frac{1}{2}} - x, 0 \leq x \leq 16

- \frac{1}{2} e^{- 2 x} x - \frac{11}{4} e^{- 2 x} + C

f (x) = 2 x e^{- x^{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))