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

The extreme f(x,y)=xy-x^2-y^2+x+y is Maximum(1,1)

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

extreme points

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

Maximum (1, 1)

Solution steps

Find the critical points:

(1, 1)

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

D (x, y) = 3

Check the sign of at each critical point

Check critical point

(1, 1) :

Maximum

Maximum (1, 1)

f (x) = 1 - x - x^{2}

f (x) = 32 y^{2} + x^{2} - x^{2} y

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

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

f (x) = x^{2} + 64

What is the extreme f(x,y)=xy-x^2-y^2+x+y ?
The extreme f(x,y)=xy-x^2-y^2+x+y is Maximum(1,1)