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)

f (x) = x^{4} - x^{3}

f (x) = \frac{10}{3} x^{3} + 13 x^{2} + 12 x + 50

9 - 2 x + 4 y - x^{2} - 4 y^{2}

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

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

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)