What is the extreme f(x,y)=2xy-5x^2-2y^2+4x+4y-4 ?

The extreme f(x,y)=2xy-5x^2-2y^2+4x+4y-4 is Maximum(2/3 , 4/3)

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extreme f(x,y)=2xy-5x^2-2y^2+4x+4y-4

extreme points

f (x, y) = 2 x y - 5 x^{2} - 2 y^{2} + 4 x + 4 y - 4

Maximum (\frac{2}{3}, \frac{4}{3})

Solution steps

Find the critical points:

(\frac{2}{3}, \frac{4}{3})

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

D (x, y) = 36

Check the sign of at each critical point

Check critical point

(\frac{2}{3}, \frac{4}{3}) :

Maximum

Maximum (\frac{2}{3}, \frac{4}{3})

w (x, y) = 6 + \frac{3 x y}{75}

f (x) = 14 x y - x^{3} - 7 y^{2}

x^{\frac{4}{3}} (7 x^{2} + 10 x - 210)

f (x) = - x^{3} + 3 x^{2} - 8

f (x) = 8 x^{2} - 2 x^{4}

What is the extreme f(x,y)=2xy-5x^2-2y^2+4x+4y-4 ?
The extreme f(x,y)=2xy-5x^2-2y^2+4x+4y-4 is Maximum(2/3 , 4/3)