What is the extreme E(X,Y)=(X+Y)^2-3(X+Y)(X-Y) ?

The extreme E(X,Y)=(X+Y)^2-3(X+Y)(X-Y) is Saddle(0,0)

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extreme E(X,Y)=(X+Y)^2-3(X+Y)(X-Y)

extreme points

E (X, Y) = (X + Y)^{2} - 3 (X + Y) (X - Y)

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial X ^{2}} = 8

D (X, Y) = - 36

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

x^{2} - 7 x + 13

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

f (x) = x^{3} - 6 x^{2} + 9 x - 7

f (x) = 2 x^{5} - x^{4} - 9 x^{3} + 13 x^{2} - 5 x

y = \frac{( x + 1 )}{x ^{2} + 4 x - 5}

What is the extreme E(X,Y)=(X+Y)^2-3(X+Y)(X-Y) ?
The extreme E(X,Y)=(X+Y)^2-3(X+Y)(X-Y) is Saddle(0,0)