What is the extreme f(x,y)=2x^3+2y^3-9x^2+3y^2-13y ?

The extreme f(x,y)=2x^3+2y^3-9x^2+3y^2-13y is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x,y)=2x^3+2y^3-9x^2+3y^2-13y

extreme points

f (x, y) = 2 x^{3} + 2 y^{3} - 9 x^{2} + 3 y^{2} - 13 y

Saddle (0, \frac{- 3 + 87}{6}), Maximum (0, - \frac{3 + 87}{6}), Minimum (3, \frac{- 3 + 87}{6}), Saddle (3, - \frac{3 + 87}{6})

Solution steps

Find the critical points:

(0, \frac{- 3 + 87}{6}), (0, - \frac{3 + 87}{6}), (3, \frac{- 3 + 87}{6}), (3, - \frac{3 + 87}{6})

\frac{\partial ^{2} f}{\partial x ^{2}} = 12 y + 6

D (x, y) = (12 y + 6) (12 x - 18)

Check the sign of at each critical point

Check critical point

(0, \frac{- 3 + 87}{6}) :

Saddle

Check critical point

(0, - \frac{3 + 87}{6}) :

Maximum

Check critical point

(3, \frac{- 3 + 87}{6}) :

Minimum

Check critical point

(3, - \frac{3 + 87}{6}) :

Saddle

Saddle (0, \frac{- 3 + 87}{6}), Maximum (0, - \frac{3 + 87}{6}), Minimum (3, \frac{- 3 + 87}{6}), Saddle (3, - \frac{3 + 87}{6})

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

f (x) = - x^{2} + 1, - 1 \leq x \leq 2

f (x) = - x + 3 x + 5

f (x, y) = x^{3} + y^{3} + 3 x^{2} - 6 y^{2}

- 2 + 2 x - x^{2}

What is the extreme f(x,y)=2x^3+2y^3-9x^2+3y^2-13y ?
The extreme f(x,y)=2x^3+2y^3-9x^2+3y^2-13y is