What is the extreme f(x,y)=-3x^2-2xy-2y^2+400x+200y ?

The extreme f(x,y)=-3x^2-2xy-2y^2+400x+200y is Maximum(60,20)

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extreme f(x,y)=-3x^2-2xy-2y^2+400x+200y

extreme points

f (x, y) = - 3 x^{2} - 2 x y - 2 y^{2} + 400 x + 200 y

Maximum (60, 20)

Solution steps

Find the critical points:

(60, 20)

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

D (x, y) = 20

Check the sign of at each critical point

Check critical point

(60, 20) :

Maximum

Maximum (60, 20)

f (x, y) = 2 - 5 x^{2} - 2 y^{2}

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

y = 4 - x^{2}

2 cos (x) + sin (2 x)

f (x) = x^{3} - 18 x^{2} + 81 x + 45

What is the extreme f(x,y)=-3x^2-2xy-2y^2+400x+200y ?
The extreme f(x,y)=-3x^2-2xy-2y^2+400x+200y is Maximum(60,20)