en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme-3x^5+5x^3

Solution

extreme points

- 3 x^{5} + 5 x^{3}

Solution

Minimum (- 1, - 2), Saddle (0, 0), Maximum (1, 2)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

- 3 x^{5} + 5 x^{3} : - 2

Minimum (- 1, - 2)

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 1

into

- 3 x^{5} + 5 x^{3} : 2

Maximum (1, 2)

Minimum (- 1, - 2), Saddle (0, 0), Maximum (1, 2)

Graph

Popular Examples

extreme f(x,y)=(x-y)(16-xy)

extreme f(x,y)=(1+xy)(x+y)

extreme f(x)=3x^4-4x^3-12x^2+1

extreme f(x)=x^3-3x^2-24x+2

extreme f(x)=(x^2)/(sqrt(x+1))

Frequently Asked Questions (FAQ)

What is the extreme-3x^5+5x^3 ?
The extreme-3x^5+5x^3 is Minimum(-1,-2),Saddle(0,0),Maximum(1,2)