What is the extreme f(x)=x^3+x^2-x-1 ?

The extreme f(x)=x^3+x^2-x-1 is Maximum(-1,0),Minimum(1/3 ,-32/27)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=x^3+x^2-x-1

extreme points

f (x) = x^{3} + x^{2} - x - 1

Maximum (- 1, 0), Minimum (\frac{1}{3}, - \frac{32}{27})

Solution steps

f^{'} (x) = 3 x^{2} + 2 x - 1

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = - 1

into

x^{3} + x^{2} - x - 1 : 0

Maximum (- 1, 0)

Plug

x = \frac{1}{3}

into

x^{3} + x^{2} - x - 1 : - \frac{32}{27}

Minimum (\frac{1}{3}, - \frac{32}{27})

Maximum (- 1, 0), Minimum (\frac{1}{3}, - \frac{32}{27})

What is the extreme f(x)=x^3+x^2-x-1 ?
The extreme f(x)=x^3+x^2-x-1 is Maximum(-1,0),Minimum(1/3 ,-32/27)