What is the extreme f(x)= 1/9 x^4-4/9 x^3 ?

The extreme f(x)= 1/9 x^4-4/9 x^3 is Saddle(0,0),Minimum(3,-3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)= 1/9 x^4-4/9 x^3

extreme points

f (x) = \frac{1}{9} x^{4} - \frac{4}{9} x^{3}

Saddle (0, 0), Minimum (3, - 3)

Solution steps

f^{'} (x) = \frac{4 x ^{3}}{9} - \frac{4 x ^{2}}{3}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

\frac{1}{9} x^{4} - \frac{4}{9} x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

\frac{1}{9} x^{4} - \frac{4}{9} x^{3} : - 3

Minimum (3, - 3)

Saddle (0, 0), Minimum (3, - 3)

f (x) = \frac{6 x - 1}{3 x + 6}

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

x^{2} + 4 x + 5

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

y = 2 x^{2} - 3 x + 4

What is the extreme f(x)= 1/9 x^4-4/9 x^3 ?
The extreme f(x)= 1/9 x^4-4/9 x^3 is Saddle(0,0),Minimum(3,-3)