What is the extreme f(x,y)=2x^2+xy+4y^2-2x+10y ?

The extreme f(x,y)=2x^2+xy+4y^2-2x+10y is Minimum(26/31 ,-42/31)

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extreme f(x,y)=2x^2+xy+4y^2-2x+10y

extreme

Minimum (\frac{26}{31}, - \frac{42}{31})

Solution steps

Find the critical points:

(\frac{26}{31}, - \frac{42}{31})

\frac{\partial ^{2} f}{\partial x ^{2}} = 8

D (x, y) = 31

Check the sign of at each critical point

Check critical point

(\frac{26}{31}, - \frac{42}{31}) :

Minimum

Minimum (\frac{26}{31}, - \frac{42}{31})

What is the extreme f(x,y)=2x^2+xy+4y^2-2x+10y ?
The extreme f(x,y)=2x^2+xy+4y^2-2x+10y is Minimum(26/31 ,-42/31)