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

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

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extreme f(x,y)=x^2+xy+y^2+x-y+1

extreme points

f (x, y) = x^{2} + x y + y^{2} + x - y + 1

Minimum (- 1, 1)

Solution steps

Find the critical points:

(- 1, 1)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(- 1, 1) :

Minimum

Minimum (- 1, 1)

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