What is the extreme x^3-8y^3+4xy-8 ?

The extreme x^3-8y^3+4xy-8 is Saddle(0,0),Minimum(2/3 ,-1/3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x^3-8y^3+4xy-8

extreme points

x^{3} - 8 y^{3} + 4 x y - 8

Saddle (0, 0), Minimum (\frac{2}{3}, - \frac{1}{3})

Solution steps

Find the critical points:

(0, 0), (\frac{2}{3}, - \frac{1}{3})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 48 y

D (x, y) = - 288 x y - 16

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(\frac{2}{3}, - \frac{1}{3}) :

Minimum

Saddle (0, 0), Minimum (\frac{2}{3}, - \frac{1}{3})

f (x, y) = 2 x^{2} - 4 x + y^{2} - 6 y + 1

f (x) = (24 + x) (600 - 15 x)

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

f (x) = cos (x) - 6 x, 0 \leq x \leq 4 π

4 x^{3} - 12 x

What is the extreme x^3-8y^3+4xy-8 ?
The extreme x^3-8y^3+4xy-8 is Saddle(0,0),Minimum(2/3 ,-1/3)