What is the extreme f(x,y)=x^3-24x+y^3-10y ?

The extreme f(x,y)=x^3-24x+y^3-10y is

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extreme f(x,y)=x^3-24x+y^3-10y

extreme points

f (x, y) = x^{3} - 24 x + y^{3} - 10 y

Saddle (- 22, \frac{10}{3}), Maximum (- 22, - \frac{10}{3}), Minimum (22, \frac{10}{3}), Saddle (22, - \frac{10}{3}), Saddle (22, - \frac{10}{3}), Maximum (- 22, - \frac{10}{3}), Minimum (22, \frac{10}{3}), Saddle (- 22, \frac{10}{3})

Solution steps

Find the critical points:

(- 22, \frac{10}{3}), (- 22, - \frac{10}{3}), (22, \frac{10}{3}), (22, - \frac{10}{3}), (22, - \frac{10}{3}), (- 22, - \frac{10}{3}), (22, \frac{10}{3}), (- 22, \frac{10}{3})

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

D (x, y) = 36 x y

Check the sign of at each critical point

Check critical point

(- 22, \frac{10}{3}) :

Saddle

Check critical point

(- 22, - \frac{10}{3}) :

Maximum

Check critical point

(22, \frac{10}{3}) :

Minimum

Check critical point

(22, - \frac{10}{3}) :

Saddle

Check critical point

(22, - \frac{10}{3}) :

Saddle

Check critical point

(- 22, - \frac{10}{3}) :

Maximum

Check critical point

(22, \frac{10}{3}) :

Minimum

Check critical point

(- 22, \frac{10}{3}) :

Saddle

Saddle (- 22, \frac{10}{3}), Maximum (- 22, - \frac{10}{3}), Minimum (22, \frac{10}{3}), Saddle (22, - \frac{10}{3}), Saddle (22, - \frac{10}{3}), Maximum (- 22, - \frac{10}{3}), Minimum (22, \frac{10}{3}), Saddle (- 22, \frac{10}{3})

f (x) = \frac{2 x}{x ^{2} - 2 x - 3}

f (x) = \frac{x ^{2} + 3 x + 3}{x + 2}

y = x^{2} + \frac{250}{x}

f (x) = x^{2} - 10 x + 6

f (x) = 3 x^{2} + 15 x + 18

What is the extreme f(x,y)=x^3-24x+y^3-10y ?
The extreme f(x,y)=x^3-24x+y^3-10y is