en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=3x^5-3x^3

Solution

extreme points

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

Solution

Maximum (- \frac{3}{5}, - 3 (\frac{3}{5})^{\frac{5}{2}} + 3 (\frac{3}{5})^{\frac{3}{2}}), Saddle (0, 0), Minimum (\frac{3}{5}, 3 (\frac{3}{5})^{\frac{5}{2}} - 3 (\frac{3}{5})^{\frac{3}{2}})

Solution steps

f^{'} (x) = 15 x^{4} - 9 x^{2}

Find intervals:

Increasing

: - \infty < x < - \frac{3}{5},

Decreasing

: - \frac{3}{5} < x < 0,

Decreasing

: 0 < x < \frac{3}{5},

Increasing

: \frac{3}{5} < x < \infty

Plug

x = - \frac{3}{5}

into

3 x^{5} - 3 x^{3} : - 3 (\frac{3}{5})^{\frac{5}{2}} + 3 (\frac{3}{5})^{\frac{3}{2}}

Maximum (- \frac{3}{5}, - 3 (\frac{3}{5})^{\frac{5}{2}} + 3 (\frac{3}{5})^{\frac{3}{2}})

Plug

x = 0

into

3 x^{5} - 3 x^{3} : 0

Saddle (0, 0)

Plug

x = \frac{3}{5}

into

3 x^{5} - 3 x^{3} : 3 (\frac{3}{5})^{\frac{5}{2}} - 3 (\frac{3}{5})^{\frac{3}{2}}

Minimum (\frac{3}{5}, 3 (\frac{3}{5})^{\frac{5}{2}} - 3 (\frac{3}{5})^{\frac{3}{2}})

Maximum (- \frac{3}{5}, - 3 (\frac{3}{5})^{\frac{5}{2}} + 3 (\frac{3}{5})^{\frac{3}{2}}), Saddle (0, 0), Minimum (\frac{3}{5}, 3 (\frac{3}{5})^{\frac{5}{2}} - 3 (\frac{3}{5})^{\frac{3}{2}})

Popular Examples

critical 4x-x^3 critical points

4 x - x^{3}

critical x^3+x-9 critical points

x^{3} + x - 9

parity f(x)=7x^3 parity

f (x) = 7 x^{3}

parallel y=5x+13 parallel

y = 5 x + 13

inverse of f(x)=(x-1)/(x-2)inverse

f (x) = \frac{x - 1}{x - 2}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=3x^5-3x^3 ?
The extreme f(x)=3x^5-3x^3 is