What is the extreme (x-1)/(x^2+2x+6) ?

The extreme (x-1)/(x^2+2x+6) is Minimum(-2,-1/2),Maximum(4, 1/10)

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+2x+6)

extreme points

\frac{x - 1}{x ^{2} + 2 x + 6}

Minimum (- 2, - \frac{1}{2}), Maximum (4, \frac{1}{10})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 2 x + 8}{( x ^{2} + 2 x + 6 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 2

into

\frac{x - 1}{x ^{2} + 2 x + 6} : - \frac{1}{2}

Minimum (- 2, - \frac{1}{2})

Plug

x = 4

into

\frac{x - 1}{x ^{2} + 2 x + 6} : \frac{1}{10}

Maximum (4, \frac{1}{10})

Minimum (- 2, - \frac{1}{2}), Maximum (4, \frac{1}{10})

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

f (x) = 3 (x + 1)^{2} - 4

y = 2 x^{2} - 3

2 x + 6

x^{2} + 4 x + 7

What is the extreme (x-1)/(x^2+2x+6) ?
The extreme (x-1)/(x^2+2x+6) is Minimum(-2,-1/2),Maximum(4, 1/10)