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

The extreme f(x,y)=-x^2-2y^2+xy+x+3y is Maximum(1,1)

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

extreme

Maximum (1, 1)

Solution steps

Find the critical points:

(1, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 4

D (x, y) = 7

Check the sign of at each critical point

Check critical point

(1, 1) :

Maximum

Maximum (1, 1)

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