What is the extreme P(x,y)=-4x+52y-x^2+2xy-7y^2+9 ?

The extreme P(x,y)=-4x+52y-x^2+2xy-7y^2+9 is Maximum(2,4)

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extreme P(x,y)=-4x+52y-x^2+2xy-7y^2+9

extreme points

P (x, y) = - 4 x + 52 y - x^{2} + 2 x y - 7 y^{2} + 9

Maximum (2, 4)

Solution steps

Find the critical points:

(2, 4)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 14

D (x, y) = 24

Check the sign of at each critical point

Check critical point

(2, 4) :

Maximum

Maximum (2, 4)

f (x) = 40 + 160 = 200

2 x^{3} + 3 x^{2} - 336 x

f (x) = \frac{6 x}{( x ^{2} - 4 )}

f (x) = \frac{x ^{3}}{6 x ^{2} + 4}

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

What is the extreme P(x,y)=-4x+52y-x^2+2xy-7y^2+9 ?
The extreme P(x,y)=-4x+52y-x^2+2xy-7y^2+9 is Maximum(2,4)