What is the extreme f(x)=x(16-x)^3 ?

The extreme f(x)=x(16-x)^3 is Maximum(4,6912),Saddle(16,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=x(16-x)^3

extreme points

f (x) = x (16 - x)^{3}

Maximum (4, 6912), Saddle (16, 0)

Solution steps

f^{'} (x) = - 4 (x - 4) (x - 16)^{2}

Find intervals:

Increasing

: - \infty < x < 4,

Decreasing

: 4 < x < 16,

Decreasing

: 16 < x < \infty

Plug

x = 4

into

x (16 - x)^{3} : 6912

Maximum (4, 6912)

Plug

x = 16

into

x (16 - x)^{3} : 0

Saddle (16, 0)

Maximum (4, 6912), Saddle (16, 0)

- x - 1

105 - 20 sin (\frac{5 π}{4} x)

y = \frac{3 x ^{4}}{5}

y = \frac{14}{x + 3}

- \frac{5}{x}

What is the extreme f(x)=x(16-x)^3 ?
The extreme f(x)=x(16-x)^3 is Maximum(4,6912),Saddle(16,0)