What is the extreme f(x,y)=(x-3)(y-3)(x+y-3) ?

The extreme f(x,y)=(x-3)(y-3)(x+y-3) is Saddle(3,0),Maximum(2,2)

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extreme f(x,y)=(x-3)(y-3)(x+y-3)

extreme

Saddle (3, 0), Maximum (2, 2)

Solution steps

Find the critical points:

(3, 0), (2, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 (x - 3)

D (x, y) = - 4 x^{2} + 24 x - 4 x y + 24 y - 4 y^{2} - 45

Check the sign of at each critical point

Check critical point

(3, 0) :

Saddle

Check critical point

(2, 2) :

Maximum

Saddle (3, 0), Maximum (2, 2)

What is the extreme f(x,y)=(x-3)(y-3)(x+y-3) ?
The extreme f(x,y)=(x-3)(y-3)(x+y-3) is Saddle(3,0),Maximum(2,2)