What is the extreme f(x,y)=2xy-x^2-6y^2+4x+1 ?

The extreme f(x,y)=2xy-x^2-6y^2+4x+1 is Maximum(12/5 , 2/5)

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extreme f(x,y)=2xy-x^2-6y^2+4x+1

extreme

Maximum (\frac{12}{5}, \frac{2}{5})

Solution steps

Find the critical points:

(\frac{12}{5}, \frac{2}{5})

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

D (x, y) = 20

Check the sign of at each critical point

Check critical point

(\frac{12}{5}, \frac{2}{5}) :

Maximum

Maximum (\frac{12}{5}, \frac{2}{5})

What is the extreme f(x,y)=2xy-x^2-6y^2+4x+1 ?
The extreme f(x,y)=2xy-x^2-6y^2+4x+1 is Maximum(12/5 , 2/5)