What is the extreme f(x,y)=xy+e^{xy} ?

The extreme f(x,y)=xy+e^{xy} is Saddle(0,0)

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extreme f(x,y)=xy+e^{xy}

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x, y) = x^{3} + 3 \cdot x \cdot y - y^{2}

f (x) = 4 ln (2 x e^{- x})

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

f (x) = \frac{y - 3}{y ^{2} - 3 y + 9}

f (x) = (16 - x) (100 x + 1300)

What is the extreme f(x,y)=xy+e^{xy} ?
The extreme f(x,y)=xy+e^{xy} is Saddle(0,0)