What is the extreme f(x,y)=3+xy-x-2y ?

The extreme f(x,y)=3+xy-x-2y is Saddle(2,1)

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extreme f(x,y)=3+xy-x-2y

extreme points

f (x, y) = 3 + x y - x - 2 y

Saddle (2, 1)

Solution steps

Find the critical points:

(2, 1)

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

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(2, 1) :

Saddle

Saddle (2, 1)

f (x, y) = x^{3} + 6 x y + y^{3} + 3

f (x, y) = 3 x y^{2} - 2 y + 5 x^{2} y^{2}

x^{4} - 6 x^{2}

f (x) = x^{2} - 8 x + 12

f (x) = x^{3} - 3 x^{2} - 9 x + 7

What is the extreme f(x,y)=3+xy-x-2y ?
The extreme f(x,y)=3+xy-x-2y is Saddle(2,1)