What is the extreme f(x)=x(10-2x)(8-x) ?

The extreme f(x)=x(10-2x)(8-x) is Maximum(2,72),Minimum(20/3 ,-800/27)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=x(10-2x)(8-x)

extreme points

f (x) = x (10 - 2 x) (8 - x)

Maximum (2, 72), Minimum (\frac{20}{3}, - \frac{800}{27})

Solution steps

f^{'} (x) = 2 (x - 2) (3 x - 20)

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < \frac{20}{3},

Increasing

: \frac{20}{3} < x < \infty

Plug

x = 2

into

x (10 - 2 x) (8 - x) : 72

Maximum (2, 72)

Plug

x = \frac{20}{3}

into

x (10 - 2 x) (8 - x) : - \frac{800}{27}

Minimum (\frac{20}{3}, - \frac{800}{27})

Maximum (2, 72), Minimum (\frac{20}{3}, - \frac{800}{27})

What is the extreme f(x)=x(10-2x)(8-x) ?
The extreme f(x)=x(10-2x)(8-x) is Maximum(2,72),Minimum(20/3 ,-800/27)