What is the extreme f(x,y)=xy-x^2-y^2+3+9y ?

The extreme f(x,y)=xy-x^2-y^2+3+9y is Maximum(3,6)

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extreme f(x,y)=xy-x^2-y^2+3+9y

extreme points

f (x, y) = x y - x^{2} - y^{2} + 3 + 9 y

Maximum (3, 6)

Solution steps

Find the critical points:

(3, 6)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(3, 6) :

Maximum

Maximum (3, 6)

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

f (0) = x^{2} - 2 x - 3

x^{4} - 16 x^{2} + 3

f (x) = 8 - 5 x + x^{2}

\frac{1}{3} x^{3} - 9 x^{2} + 72 x + 2

What is the extreme f(x,y)=xy-x^2-y^2+3+9y ?
The extreme f(x,y)=xy-x^2-y^2+3+9y is Maximum(3,6)