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 points

f (x, y) = 2 x y - x^{2} - 6 y^{2} + 4 x + 1

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})

f (x) = - x^{2} - 2 x + 99

f (x) = - x^{2} + 5, - 3 \leq x \leq 4

f (x) = x^{\frac{2}{3}} (x - 1), - 1 \leq x \leq 1

f (x, y) = 4 x^{3} + 2 y^{2} - 24 x^{2} + 2 y + 8

\frac{8 x}{1 - x}

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)