What is the extreme f(x,y)=xy-2x-y+6 ?

The extreme f(x,y)=xy-2x-y+6 is Saddle(1,2)

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extreme f(x,y)=xy-2x-y+6

extreme points

f (x, y) = x y - 2 x - y + 6

Saddle (1, 2)

Solution steps

Find the critical points:

(1, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(1, 2) :

Saddle

Saddle (1, 2)

f (x) = - (x - 1)^{2}

f (x) = \frac{( - 2 x ^{2} + 5 x - 1 )}{2 x - 1}

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

f (x, y) = 4 x + 6 y - x^{2} - y^{2} + 8

f (x) = x^{3} + 6 x^{2} + 8

What is the extreme f(x,y)=xy-2x-y+6 ?
The extreme f(x,y)=xy-2x-y+6 is Saddle(1,2)