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(x-4)^3

Solution

extreme points

f (x) = x (x - 4)^{3}

Solution

Minimum (1, - 27), Saddle (4, 0)

Solution steps

f^{'} (x) = 4 (x - 4)^{2} (x - 1)

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 1

into

x (x - 4)^{3} : - 27

Minimum (1, - 27)

Plug

x = 4

into

x (x - 4)^{3} : 0

Saddle (4, 0)

Minimum (1, - 27), Saddle (4, 0)

Popular Examples

inverse of f(x)=-4+7/2 x inverse

f (x) = - 4 + \frac{7}{2} x

slope ofintercept 2x-3y=-12 slope intercept

2 x - 3 y = - 12

midpoint (-3,-9),(0,-12)midpoint

(- 3, - 9), (0, - 12)

range of \sqrt[3]{x-12}range

inflection f(x)=sin^2(2x)inflection points

f (x) = sin^{2} (2 x)

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(x-4)^3 ?
The extreme f(x)=x(x-4)^3 is Minimum(1,-27),Saddle(4,0)