What is the extreme R(x,y)=-5x^2-8y^2-2xy+42x+102y ?

The extreme R(x,y)=-5x^2-8y^2-2xy+42x+102y is Maximum(3,6)

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extreme R(x,y)=-5x^2-8y^2-2xy+42x+102y

extreme points

R (x, y) = - 5 x^{2} - 8 y^{2} - 2 x y + 42 x + 102 y

Maximum (3, 6)

Solution steps

Find the critical points:

(3, 6)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 16

D (x, y) = 156

Check the sign of at each critical point

Check critical point

(3, 6) :

Maximum

Maximum (3, 6)

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

4 x^{2} - 4 x

f (x) = 2 x^{3} - 4 x^{2} - 3

f (x) = 2 - 2 cos (x)

\frac{1}{x ^{2}} + \frac{4}{y ^{2}} + 4 x y^{2}

What is the extreme R(x,y)=-5x^2-8y^2-2xy+42x+102y ?
The extreme R(x,y)=-5x^2-8y^2-2xy+42x+102y is Maximum(3,6)