What is the extreme f(x)=x^2+xy+y^2-13y+56 ?

The extreme f(x)=x^2+xy+y^2-13y+56 is Minimum(-13/3 , 26/3)

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extreme f(x)=x^2+xy+y^2-13y+56

extreme

Minimum (- \frac{13}{3}, \frac{26}{3})

Solution steps

Find the critical points:

(- \frac{13}{3}, \frac{26}{3})

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(- \frac{13}{3}, \frac{26}{3}) :

Minimum

Minimum (- \frac{13}{3}, \frac{26}{3})

What is the extreme f(x)=x^2+xy+y^2-13y+56 ?
The extreme f(x)=x^2+xy+y^2-13y+56 is Minimum(-13/3 , 26/3)