What is the extreme P(x,y)=8x+10y-1(x^2+xy+y^2)-10000 ?

The extreme P(x,y)=8x+10y-1(x^2+xy+y^2)-10000 is Maximum(2,4)

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extreme P(x,y)=8x+10y-1(x^2+xy+y^2)-10000

extreme points

P (x, y) = 8 x + 10 y - 1 (x^{2} + x y + y^{2}) - 10000

Maximum (2, 4)

Solution steps

Find the critical points:

(2, 4)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(2, 4) :

Maximum

Maximum (2, 4)

f (x, y) = 3 x^{4} + 8 x^{3} - 18 x^{2} + 6 y^{2} + 12 y - 4

f (x) = - x^{3} + 3 x^{2} + 45 x - 7

f (x) = \frac{3 x ^{2}}{x + 5}

f (x) = 4 x^{2} + y^{2} - 12 x - 6 y - 2 x y + 3

f (x) = 2 y - 2 - x

What is the extreme P(x,y)=8x+10y-1(x^2+xy+y^2)-10000 ?
The extreme P(x,y)=8x+10y-1(x^2+xy+y^2)-10000 is Maximum(2,4)