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

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

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

extreme points

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

x, f = \frac{20000}{3 + x ^{2} + y ^{2}}

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

y = - 4 e^{- 4 t} - 5 e^{- 5 t}

f (x) = x^{4} - 24 x^{2} + 23

\frac{( x ^{2} - 5 ) ^{3}}{125}

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