What is the extreme f(x,y)=4x+6y-x^2-y^2 ?

The extreme f(x,y)=4x+6y-x^2-y^2 is Maximum(2,3)

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extreme f(x,y)=4x+6y-x^2-y^2

extreme points

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

Maximum (2, 3)

Solution steps

Find the critical points:

(2, 3)

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

D (x, y) = 4

Check the sign of at each critical point

Check critical point

(2, 3) :

Maximum

Maximum (2, 3)

f (x) = x^{2} + 4 x + 16

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

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

\frac{x ^{3} - 3 x}{x ^{2} - 1}

f (x, y) = x^{3} - 6 x y + 8 y^{3}

What is the extreme f(x,y)=4x+6y-x^2-y^2 ?
The extreme f(x,y)=4x+6y-x^2-y^2 is Maximum(2,3)