What is the extreme ((x-1))/((x^2-x+1)) ?

The extreme ((x-1))/((x^2-x+1)) is Minimum(0,-1),Maximum(2, 1/3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme ((x-1))/((x^2-x+1))

extreme points

\frac{( x - 1 )}{( x ^{2} - x + 1 )}

Minimum (0, - 1), Maximum (2, \frac{1}{3})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

\frac{x - 1}{x ^{2} - x + 1} : - 1

Minimum (0, - 1)

Plug

x = 2

into

\frac{x - 1}{x ^{2} - x + 1} : \frac{1}{3}

Maximum (2, \frac{1}{3})

Minimum (0, - 1), Maximum (2, \frac{1}{3})

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

f (x, y) = x^{3} - 3 x + y^{2} - y^{4}

f (x) = (x - 10)^{\frac{1}{3}}

y = (2 x - 1)^{2}

f (x) = 3 x + \frac{147}{x}

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