What is the extreme f(x,y)= 1/((1+x*y)) ?

The extreme f(x,y)= 1/((1+x*y)) is Saddle(0,0)

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extreme f(x,y)= 1/((1+x*y))

extreme

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = \frac{3 x y - 1}{( 1 + x y ) ^{5}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

What is the extreme f(x,y)= 1/((1+x*y)) ?
The extreme f(x,y)= 1/((1+x*y)) is Saddle(0,0)