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})

y = \frac{x}{1 + x ^{2}}

\frac{x ^{2} - 1}{x ^{2} - 4}

f (x) = 5 x^{2} ln (x)

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

f (x) = 2 x^{3} + 9 x^{2} + 1

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)