en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme x(x-4)^3

Solution

extreme points

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

midpoint (-3,-1),(-8,6)midpoint

(- 3, - 1), (- 8, 6)

y = - x^{2} + 4 x + 1

shift f(x)=-3sin(2x+pi/2)shift

f (x) = - 3 sin (2 x + \frac{π}{2})

line (6,0),(0,10)line

(6, 0), (0, 10)

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

f (x) = \frac{2}{x ^{2} + 1}

Frequently Asked Questions (FAQ)

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