What is the extreme U(x,y)=-x^2-3y^2+2xy+100x ?

The extreme U(x,y)=-x^2-3y^2+2xy+100x is Maximum(75,25)

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extreme U(x,y)=-x^2-3y^2+2xy+100x

extreme points

U (x, y) = - x^{2} - 3 y^{2} + 2 x y + 100 x

Maximum (75, 25)

Solution steps

Find the critical points:

(75, 25)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 6

D (x, y) = 8

Check the sign of at each critical point

Check critical point

(75, 25) :

Maximum

Maximum (75, 25)

f (x) = x^{2} + \frac{120}{x}

f (x, y) = \frac{1}{2} y^{4} - 4 x y + 2 x^{4}

f (x) = 2 x^{5} ln (x)

f (x) = 48 x^{3} + 57 x^{2} - 54 x + 18

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

What is the extreme U(x,y)=-x^2-3y^2+2xy+100x ?
The extreme U(x,y)=-x^2-3y^2+2xy+100x is Maximum(75,25)