What is the extreme f(x,y)=xy-x^2-y^2+x+y+17 ?

The extreme f(x,y)=xy-x^2-y^2+x+y+17 is Maximum(1,1)

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extreme f(x,y)=xy-x^2-y^2+x+y+17

extreme points

f (x, y) = x y - x^{2} - y^{2} + x + y + 17

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) = 50 y^{2} + x^{2} - x^{2} y

f (x) = 8 x^{\frac{3}{4}} - x, 0 \leq x \leq 4096

\frac{x ^{2} - 7}{x + 4}

f (x) = \frac{x ^{3}}{3} + 4 x^{2} + 15 x + 7

T (x, y) = \frac{x ^{3} + y ^{3}}{( x + y ) ^{2} - 3 x y} - x

What is the extreme f(x,y)=xy-x^2-y^2+x+y+17 ?
The extreme f(x,y)=xy-x^2-y^2+x+y+17 is Maximum(1,1)