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

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

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

extreme points

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

Minimum (- 1, 1)

Solution steps

Find the critical points:

(- 1, 1)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(- 1, 1) :

Minimum

Minimum (- 1, 1)

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