What is the extreme x^2+2xy+2y^2+2x-2y ?

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

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extreme x^2+2xy+2y^2+2x-2y

extreme points

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)

f (x) = t^{3} - 15 t^{2} + 72 t + 8

f (x) = \frac{7}{12} x^{3} + 7 x^{2} + 21 x + 9

R (x, y) = - 5 x^{2} - 4 y^{2} - 4 x y + 68 x + 72 y

f (x, y) = 9 - x^{2} - 2 y^{2}

y = x^{2} - 6 x + 5

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