What is the extreme f(x)=((x+y-xy)/(x-y+xy)) ?

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

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extreme f(x)=((x+y-xy)/(x-y+xy))

extreme points

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

Saddle (1, 0)

Solution steps

Find the critical points:

(1, 0)

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

D (x, y) = \frac{16 x ^{3} y ^{2} + 16 x ^{3} y - 36 x ^{2} y ^{2} - 24 x ^{2} y - 4 x ^{2} + 24 x y ^{2} + 8 x y - 4 y ^{2}}{( x - y + x y ) ^{6}}

Check the sign of at each critical point

Check critical point

(1, 0) :

Saddle

Saddle (1, 0)

3 (x + 2) (x - 10)

f (x, y) = 1 - x^{2} - x - 3 y^{2} + y

f (x) = 1.4 t e^{- 2.9 t}

f (x) = 2 x^{3} - 9 x^{2} - 24 x + 9, - 2 \leq x \leq 5

f (x) = \frac{9 x}{x - 4}

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