What is the extreme f(x,y)=sqrt((1-xy)) ?

The extreme f(x,y)=sqrt((1-xy)) is Saddle(0,0)

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extreme f(x,y)=sqrt((1-xy))

extreme points

f (x, y) = (1 - x y)

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{x ^{2}}{4 ( 1 - x y ) ^{\frac{3}{2}}}

D (x, y) = - \frac{1}{4 ( x y - 1 ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = x^{3} - 15 x^{2} + 27 x - 8

f (x) = 2 x + 37 x^{\frac{2}{37}}

f (x, y) = 11 - 7 x + 9 y

y = 9 x^{2}

f (x) = x^{3} - 17 x^{2} - 24 x

What is the extreme f(x,y)=sqrt((1-xy)) ?
The extreme f(x,y)=sqrt((1-xy)) is Saddle(0,0)