What is the extreme R(x,y)=-5x^2-4y^2-4xy+68x+72y ?

The extreme R(x,y)=-5x^2-4y^2-4xy+68x+72y is Maximum(4,7)

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extreme R(x,y)=-5x^2-4y^2-4xy+68x+72y

extreme points

R (x, y) = - 5 x^{2} - 4 y^{2} - 4 x y + 68 x + 72 y

Maximum (4, 7)

Solution steps

Find the critical points:

(4, 7)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 8

D (x, y) = 64

Check the sign of at each critical point

Check critical point

(4, 7) :

Maximum

Maximum (4, 7)

f (x, y) = 9 - x^{2} - 2 y^{2}

y = x^{2} - 6 x + 5

\frac{d}{d t} (- 4.9 t^{2} + x + 21)

y = x^{2} + 2 x - 2

f (x, y) = 98 y^{2} + x^{2} - x^{2} y

What is the extreme R(x,y)=-5x^2-4y^2-4xy+68x+72y ?
The extreme R(x,y)=-5x^2-4y^2-4xy+68x+72y is Maximum(4,7)