What is the extreme f(x,y)=18xy-3x^2y-2xy^2 ?

The extreme f(x,y)=18xy-3x^2y-2xy^2 is Saddle(0,9),Maximum(2,3)

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extreme f(x,y)=18xy-3x^2y-2xy^2

extreme points

f (x, y) = 18 x y - 3 x^{2} y - 2 x y^{2}

Saddle (0, 9), Maximum (2, 3)

Solution steps

Find the critical points:

(0, 9), (2, 3)

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

D (x, y) = - 36 x^{2} - 24 x y + 216 x - 16 y^{2} + 144 y - 324

Check the sign of at each critical point

Check critical point

(0, 9) :

Saddle

Check critical point

(2, 3) :

Maximum

Saddle (0, 9), Maximum (2, 3)

What is the extreme f(x,y)=18xy-3x^2y-2xy^2 ?
The extreme f(x,y)=18xy-3x^2y-2xy^2 is Saddle(0,9),Maximum(2,3)