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(1-x^2)^2

Solution

extreme points

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

Solution

Maximum (- 1, 0), Minimum (- \frac{1}{5}, - \frac{16}{25 5}), Maximum (\frac{1}{5}, \frac{16}{25 5}), Minimum (1, 0)

Solution steps

f^{'} (x) = (x + 1) (x - 1) (5 x + 1) (5 x - 1)

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < - \frac{1}{5},

Increasing

: - \frac{1}{5} < x < \frac{1}{5},

Decreasing

: \frac{1}{5} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x (1 - x^{2})^{2} : 0

Maximum (- 1, 0)

Plug

x = - \frac{1}{5}

into

x (1 - x^{2})^{2} : - \frac{16}{25 5}

Minimum (- \frac{1}{5}, - \frac{16}{25 5})

Plug

x = \frac{1}{5}

into

x (1 - x^{2})^{2} : \frac{16}{25 5}

Maximum (\frac{1}{5}, \frac{16}{25 5})

Plug

x = 1

into

x (1 - x^{2})^{2} : 0

Minimum (1, 0)

Maximum (- 1, 0), Minimum (- \frac{1}{5}, - \frac{16}{25 5}), Maximum (\frac{1}{5}, \frac{16}{25 5}), Minimum (1, 0)

Popular Examples

extreme f(x)=x^3-12x^2-27x-26 extreme points

f (x) = x^{3} - 12 x^{2} - 27 x - 26

extreme f(x)= 6/(x^2+3)extreme points

f (x) = \frac{6}{x ^{2} + 3}

extreme f(x,y)=x^2-4xy+y^3+4y extreme points

f (x, y) = x^{2} - 4 x y + y^{3} + 4 y

extreme f(x)=2x^3-9x^2+2 extreme points

f (x) = 2 x^{3} - 9 x^{2} + 2

extreme f(x)=4x^3-x^2-14x-42 extreme points

f (x) = 4 x^{3} - x^{2} - 14 x - 42

Frequently Asked Questions (FAQ)

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