What is the extreme f(x,y)=-4x^2-3xy-2y^2+66x+19y+5 ?

The extreme f(x,y)=-4x^2-3xy-2y^2+66x+19y+5 is Maximum(9,-2)

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extreme f(x,y)=-4x^2-3xy-2y^2+66x+19y+5

extreme points

f (x, y) = - 4 x^{2} - 3 x y - 2 y^{2} + 66 x + 19 y + 5

Maximum (9, - 2)

Solution steps

Find the critical points:

(9, - 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 4

D (x, y) = 23

Check the sign of at each critical point

Check critical point

(9, - 2) :

Maximum

Maximum (9, - 2)

f (x) = x (x + 3)^{\frac{1}{2}}

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

f (x) = 4 x^{3} - 36 x^{2} + 80 x

2 x - 4

f (x) = 4 x^{3} - 36 x^{2} + 81 x

What is the extreme f(x,y)=-4x^2-3xy-2y^2+66x+19y+5 ?
The extreme f(x,y)=-4x^2-3xy-2y^2+66x+19y+5 is Maximum(9,-2)