en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

extreme points

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

Solution

Maximum (\frac{3 - 2 3}{3}, \frac{12 3 - 20}{3 3} + 43 - 4), Minimum (\frac{3 + 2 3}{3}, \frac{12 3 + 20}{3 3} - 4 - 43)

Solution steps

f^{'} (x) = 3 x^{2} - 6 x - 1

Find intervals:

Increasing

: - \infty < x < - \frac{2}{3} + 1,

Decreasing

: - \frac{2}{3} + 1 < x < \frac{2}{3} + 1,

Increasing

: \frac{2}{3} + 1 < x < \infty

Plug

x = \frac{3 - 2 3}{3}

into

x^{3} - 3 x^{2} - x + 3 : \frac{12 3 - 20}{3 3} + 43 - 4

Maximum (\frac{3 - 2 3}{3}, \frac{12 3 - 20}{3 3} + 43 - 4)

Plug

x = \frac{3 + 2 3}{3}

into

x^{3} - 3 x^{2} - x + 3 : \frac{12 3 + 20}{3 3} - 4 - 43

Minimum (\frac{3 + 2 3}{3}, \frac{12 3 + 20}{3 3} - 4 - 43)

Maximum (\frac{3 - 2 3}{3}, \frac{12 3 - 20}{3 3} + 43 - 4), Minimum (\frac{3 + 2 3}{3}, \frac{12 3 + 20}{3 3} - 4 - 43)

Popular Examples

extreme f(x)=x^5+x^3 extreme points

f (x) = x^{5} + x^{3}

range of (3x)/(7x-6)range

\frac{3 x}{7 x - 6}

domain of 2x^2-3 domain

2 x^{2} - 3

domain of f(x)=-2x(x-1)(x-2)domain

f (x) = - 2 x (x - 1) (x - 2)

domain of (1-2t)/(6+t)domain

\frac{1 - 2 t}{6 + t}

Frequently Asked Questions (FAQ)

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