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)

g (x, y) = ln (x^{2} + y^{2} - 1)

f (x) = x^{3} - 3 x - 1

f (x, y) = - 3 x^{2} - 2 y^{2} + 3 x - 4 y + 5

P (x, y) = 36 x^{2} - 9 y^{2}

f (x, y) = \frac{500}{4 + x ^{2} + y ^{2}}

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