What is the extreme f(x,y)=-5x^2-5xy-7y^2+50x-67y+9 ?

The extreme f(x,y)=-5x^2-5xy-7y^2+50x-67y+9 is Maximum(9,-8)

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extreme f(x,y)=-5x^2-5xy-7y^2+50x-67y+9

extreme points

f (x, y) = - 5 x^{2} - 5 x y - 7 y^{2} + 50 x - 67 y + 9

Maximum (9, - 8)

Solution steps

Find the critical points:

(9, - 8)

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

D (x, y) = 115

Check the sign of at each critical point

Check critical point

(9, - 8) :

Maximum

Maximum (9, - 8)

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

\frac{x ^{2}}{x ^{2} + 2}

f (x, y) = x^{2} - 2 y^{2} + 3 x y

f (x) = x^{2} y + x y^{2} + 4 x y - 5 y + 3

f (x, y) = 3 x^{2} - 5 y^{2}

What is the extreme f(x,y)=-5x^2-5xy-7y^2+50x-67y+9 ?
The extreme f(x,y)=-5x^2-5xy-7y^2+50x-67y+9 is Maximum(9,-8)