What is the extreme f(x)=x^5+10x^4+25x^3 ?

The extreme f(x)=x^5+10x^4+25x^3 is Maximum(-5,0),Minimum(-3,-108),Saddle(0,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=x^5+10x^4+25x^3

extreme points

f (x) = x^{5} + 10 x^{4} + 25 x^{3}

Maximum (- 5, 0), Minimum (- 3, - 108), Saddle (0, 0)

Solution steps

f^{'} (x) = 5 x^{4} + 40 x^{3} + 75 x^{2}

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 5

into

x^{5} + 10 x^{4} + 25 x^{3} : 0

Maximum (- 5, 0)

Plug

x = - 3

into

x^{5} + 10 x^{4} + 25 x^{3} : - 108

Minimum (- 3, - 108)

Plug

x = 0

into

x^{5} + 10 x^{4} + 25 x^{3} : 0

Saddle (0, 0)

Maximum (- 5, 0), Minimum (- 3, - 108), Saddle (0, 0)

What is the extreme f(x)=x^5+10x^4+25x^3 ?
The extreme f(x)=x^5+10x^4+25x^3 is Maximum(-5,0),Minimum(-3,-108),Saddle(0,0)