What is the extreme f(x,y)=20x+64y+8xy-x^2-32y^2 ?

The extreme f(x,y)=20x+64y+8xy-x^2-32y^2 is Maximum(28, 9/2)

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extreme f(x,y)=20x+64y+8xy-x^2-32y^2

extreme points

f (x, y) = 20 x + 64 y + 8 x y - x^{2} - 32 y^{2}

Maximum (28, \frac{9}{2})

Solution steps

Find the critical points:

(28, \frac{9}{2})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 64

D (x, y) = 64

Check the sign of at each critical point

Check critical point

(28, \frac{9}{2}) :

Maximum

Maximum (28, \frac{9}{2})

What is the extreme f(x,y)=20x+64y+8xy-x^2-32y^2 ?
The extreme f(x,y)=20x+64y+8xy-x^2-32y^2 is Maximum(28, 9/2)