What is the extreme f(x,y)=6x^2y-9xy ?

The extreme f(x,y)=6x^2y-9xy is Saddle(3/2 ,0),Saddle(0,0)

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extreme f(x,y)=6x^2y-9xy

extreme points

f (x, y) = 6 x^{2} y - 9 x y

Saddle (\frac{3}{2}, 0), Saddle (0, 0)

Solution steps

Find the critical points:

(\frac{3}{2}, 0), (0, 0)

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

D (x, y) = - 144 x^{2} + 216 x - 81

Check the sign of at each critical point

Check critical point

(\frac{3}{2}, 0) :

Saddle

Check critical point

(0, 0) :

Saddle

Saddle (\frac{3}{2}, 0), Saddle (0, 0)

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

x + 2 - x^{2}

f (x) = 12 x^{4} - 80 x^{3} - 24 x^{2} + 240 x + 720

y = \frac{2 ( x + 3 )}{x ^{2} + x - 2}

f (x, y) = ln (x) + y^{3}

What is the extreme f(x,y)=6x^2y-9xy ?
The extreme f(x,y)=6x^2y-9xy is Saddle(3/2 ,0),Saddle(0,0)