en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme 13x(x-1)^3

Solution

extreme points

13 x (x - 1)^{3}

Solution

Minimum (\frac{1}{4}, - \frac{351}{256}), Saddle (1, 0)

Solution steps

f^{'} (x) = 13 ((x - 1)^{3} + 3 x (x - 1)^{2})

Find intervals:

Decreasing

: - \infty < x < \frac{1}{4},

Increasing

: \frac{1}{4} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = \frac{1}{4}

into

13 x (x - 1)^{3} : - \frac{351}{256}

Minimum (\frac{1}{4}, - \frac{351}{256})

Plug

x = 1

into

13 x (x - 1)^{3} : 0

Saddle (1, 0)

Minimum (\frac{1}{4}, - \frac{351}{256}), Saddle (1, 0)

Graph

Popular Examples

domain of f(x)=(sqrt(2x+7))/(x-1)

domain of x/(4x+9)

inverse of f(x)=2^{x^5-1}

inverse of-4x^5-4

domain of (2x)/(x^2-1)

Frequently Asked Questions (FAQ)

What is the extreme 13x(x-1)^3 ?
The extreme 13x(x-1)^3 is Minimum(1/4 ,-351/256),Saddle(1,0)