What is the extreme f(x,y)=(x-y)(4-xy) ?

The extreme f(x,y)=(x-y)(4-xy) is Saddle(2,2),Saddle(-2,-2)

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extreme f(x,y)=(x-y)(4-xy)

extreme points

f (x, y) = (x - y) (4 - x y)

Saddle (2, 2), Saddle (- 2, - 2)

Solution steps

Find the critical points:

(2, 2), (- 2, - 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 x

D (x, y) = - 4 x^{2} + 4 x y - 4 y^{2}

Check the sign of at each critical point

Check critical point

(2, 2) :

Saddle

Check critical point

(- 2, - 2) :

Saddle

Saddle (2, 2), Saddle (- 2, - 2)

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

x^{4} - x^{3}

x^{6} (x - 4)^{5}

2 x^{2} + 3

f (x) = 2 x^{3} - 6 x^{2}

What is the extreme f(x,y)=(x-y)(4-xy) ?
The extreme f(x,y)=(x-y)(4-xy) is Saddle(2,2),Saddle(-2,-2)