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

The extreme f(x,y)=2x^2+xy+y^2-x-3y is Minimum(-1/7 , 11/7)

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

extreme

Minimum (- \frac{1}{7}, \frac{11}{7})

Solution steps

Find the critical points:

(- \frac{1}{7}, \frac{11}{7})

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

D (x, y) = 7

Check the sign of at each critical point

Check critical point

(- \frac{1}{7}, \frac{11}{7}) :

Minimum

Minimum (- \frac{1}{7}, \frac{11}{7})

What is the extreme f(x,y)=2x^2+xy+y^2-x-3y ?
The extreme f(x,y)=2x^2+xy+y^2-x-3y is Minimum(-1/7 , 11/7)