What is the extreme f(x,y)=x^2-4xy+y^2+6y+2 ?

The extreme f(x,y)=x^2-4xy+y^2+6y+2 is Saddle(2,1)

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extreme f(x,y)=x^2-4xy+y^2+6y+2

extreme points

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

Saddle (2, 1)

Solution steps

Find the critical points:

(2, 1)

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

D (x, y) = - 12

Check the sign of at each critical point

Check critical point

(2, 1) :

Saddle

Saddle (2, 1)

What is the extreme f(x,y)=x^2-4xy+y^2+6y+2 ?
The extreme f(x,y)=x^2-4xy+y^2+6y+2 is Saddle(2,1)