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

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

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

extreme points

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

Saddle (0, 6), Saddle (0, - 6), Minimum (\frac{2 6}{5}, \frac{6}{5}), Maximum (- \frac{2 6}{5}, - \frac{6}{5})

Solution steps

Find the critical points:

(0, 6), (0, - 6), (\frac{2 6}{5}, \frac{6}{5}), (- \frac{2 6}{5}, - \frac{6}{5})

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

D (x, y) = 6 x (6 x + 6 y) - 36 y^{2}

Check the sign of at each critical point

Check critical point

(0, 6) :

Saddle

Check critical point

(0, - 6) :

Saddle

Check critical point

(\frac{2 6}{5}, \frac{6}{5}) :

Minimum

Check critical point

(- \frac{2 6}{5}, - \frac{6}{5}) :

Maximum

Saddle (0, 6), Saddle (0, - 6), Minimum (\frac{2 6}{5}, \frac{6}{5}), Maximum (- \frac{2 6}{5}, - \frac{6}{5})

f (x) = 2 x^{4} - 36 x^{2}

f (x) = 25 (x^{2} - y^{2}) - 2 (x^{2} + y^{2})^{2}

f (x) = 2 x^{3} + 4 x^{2} + 2 x

f (x, y) = 80 x^{\frac{4}{10}} y^{\frac{2}{10}}

5 (x - 4)^{\frac{2}{3}}

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