What is the extreme U(x,y)=2x(1-y) ?

The extreme U(x,y)=2x(1-y) is Saddle(0,1)

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extreme U(x,y)=2x(1-y)

extreme points

U (x, y) = 2 x (1 - y)

Saddle (0, 1)

Solution steps

Find the critical points:

(0, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 4

Check the sign of at each critical point

Check critical point

(0, 1) :

Saddle

Saddle (0, 1)

f (x) = 4 x^{3} - x^{2} - x + 8

f (x) = - 3 sec (x)

x x - 2

f (x) = y^{3} - 3 y x^{2} - 3 y^{2} - 3 x^{2} + 1

3 - x^{2}