What is the extreme f(x,y)=x^3-27xy+27y^3 ?

The extreme f(x,y)=x^3-27xy+27y^3 is Saddle(0,0),Minimum(3,1)

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extreme f(x,y)=x^3-27xy+27y^3

extreme points

f (x, y) = x^{3} - 27 x y + 27 y^{3}

Saddle (0, 0), Minimum (3, 1)

Solution steps

Find the critical points:

(0, 0), (3, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 162 y

D (x, y) = 972 x y - 729

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(3, 1) :

Minimum

Saddle (0, 0), Minimum (3, 1)

f (x) = \frac{x ^{2} - 14 x + 49}{x - 9}

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

f (x) = x y^{2} - 8 x y

\frac{5 - x}{2 x + 6}

f (x, y) = \frac{x y}{5 x ^{2} + 2 y ^{2} + 2 x y + 1}

What is the extreme f(x,y)=x^3-27xy+27y^3 ?
The extreme f(x,y)=x^3-27xy+27y^3 is Saddle(0,0),Minimum(3,1)