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

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

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

extreme points

f (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^{- 2 x y} x y - e^{- 2 x y}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = \frac{1}{x + 3} - \frac{1}{( x + 3 ) ^{2}}

w (x, y) = 6 (x + y)

f (x) = \frac{- cos ( 2 x )}{2} - 2 sin (x)

4 e^{2 x^{2} + 5 x + 16}

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