What is the extreme 2xy-5x^2-2y^2+4x+4y-4 ?

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

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extreme 2xy-5x^2-2y^2+4x+4y-4

extreme points

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})

f (x) = 9 x e^{- x}

f (x) = - x^{3} + 12 x - 7

f (x) = x^{2} - 11, - 2 \leq x \leq 4

f (x) = 3 x^{3} - 36 x^{2} + 108 x + 8

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

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