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

The extreme f(x,y)=x^2+2xy+2y^2+2x-2y is Minimum(-3,2)

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

extreme points

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

Minimum (- 3, 2)

Solution steps

Find the critical points:

(- 3, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 4

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(- 3, 2) :

Minimum

Minimum (- 3, 2)

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