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

The extreme f(x)=x^3+y^3-27xy is Saddle(0,0),Minimum(9,9)

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

extreme points

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

Saddle (0, 0), Minimum (9, 9)

Solution steps

Find the critical points:

(0, 0), (9, 9)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 y

D (x, y) = 36 x y - 729

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(9, 9) :

Minimum

Saddle (0, 0), Minimum (9, 9)

- \frac{6}{x - 7}

f (x, y) = (x - y) (x y - 1)

f (x) = 9 x^{3} - 54 x^{2} + 81 x + 13

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

f (x) = ln (x^{2} - 1)

What is the extreme f(x)=x^3+y^3-27xy ?
The extreme f(x)=x^3+y^3-27xy is Saddle(0,0),Minimum(9,9)