en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme x^3-3x^2-x+4

Solution

extreme points

x^{3} - 3 x^{2} - x + 4

Solution

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

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

Plug

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

into

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

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

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

Graph

Popular Examples

shift f(x)=4sin(2x-pi)

inverse of f(x)=4x^2-5

asymptotes of f(x)=-4^{x+5}

slope of y=-3/4 x-3/2

domain of f(x)=2(x-3)^2+4

Frequently Asked Questions (FAQ)

What is the extreme x^3-3x^2-x+4 ?
The extreme x^3-3x^2-x+4 is