What is the extreme f(x,y)=(x-y)^2+y^2+(6-x-2y)^2 ?

The extreme f(x,y)=(x-y)^2+y^2+(6-x-2y)^2 is Minimum(24/11 , 18/11)

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extreme f(x,y)=(x-y)^2+y^2+(6-x-2y)^2

extreme

Minimum (\frac{24}{11}, \frac{18}{11})

Solution steps

Find the critical points:

(\frac{24}{11}, \frac{18}{11})

\frac{\partial ^{2} f}{\partial x ^{2}} = 12

D (x, y) = 44

Check the sign of at each critical point

Check critical point

(\frac{24}{11}, \frac{18}{11}) :

Minimum

Minimum (\frac{24}{11}, \frac{18}{11})

What is the extreme f(x,y)=(x-y)^2+y^2+(6-x-2y)^2 ?
The extreme f(x,y)=(x-y)^2+y^2+(6-x-2y)^2 is Minimum(24/11 , 18/11)