What is the extreme f(x,y)=xy^2-27xy-27y^2 ?

The extreme f(x,y)=xy^2-27xy-27y^2 is Saddle(0,0),Saddle(54,27)

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extreme f(x,y)=xy^2-27xy-27y^2

extreme points

f (x, y) = x y^{2} - 27 x y - 27 y^{2}

Saddle (0, 0), Saddle (54, 27)

Solution steps

Find the critical points:

(0, 0), (54, 27)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 x - 54

D (x, y) = - 4 y^{2} + 108 y - 729

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(54, 27) :

Saddle

Saddle (0, 0), Saddle (54, 27)

f (x) = \frac{4 x - 2}{x ^{2} - 4 x + 4}

f (x) = ln (x^{2} + 7 x + 14)

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

f (x, y) = x^{2} + x y + y^{2} - 3 x - 6 y

f (x) = x^{3} - 5 x^{2} + 7 x

What is the extreme f(x,y)=xy^2-27xy-27y^2 ?
The extreme f(x,y)=xy^2-27xy-27y^2 is Saddle(0,0),Saddle(54,27)