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) = \frac{1}{7} x^{7} - x

f (x, y) = \frac{1}{x} + x y - \frac{8}{y}

f (x) = e^{x y} - x

y = 3 x^{2} - 12 x + 13

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

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