en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

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

Solution

extreme points

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

Solution

Maximum (- \frac{2}{3}, - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} + 1), Minimum (\frac{2}{3}, (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} + 1)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3},

Decreasing

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

Increasing

: \frac{2}{3} < x < \infty

Plug

x = - \frac{2}{3}

into

x^{3} - 2 x + 1 : - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} + 1

Maximum (- \frac{2}{3}, - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} + 1)

Plug

x = \frac{2}{3}

into

x^{3} - 2 x + 1 : (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} + 1

Minimum (\frac{2}{3}, (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} + 1)

Maximum (- \frac{2}{3}, - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} + 1), Minimum (\frac{2}{3}, (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} + 1)

Graph

Popular Examples

domain of f(x)= 1/2 (3)^{x+4}-5

asymptotes of f(x)=(x^2-2x-3)/(x-2)

domain of f(x)=(6+x)/(1-6x)

intercepts of f(x)=2x-5

intercepts of f(x)=1-3x-x^2

Frequently Asked Questions (FAQ)

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