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Popular >

extreme x(1-x^2)^2

Solution

extreme points

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)

Graph

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Frequently Asked Questions (FAQ)

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