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

The extreme (-2ln(x)-2)/(x^2) is Minimum(1/(sqrt(e)),-e)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme (-2ln(x)-2)/(x^2)

extreme points

\frac{- 2 ln ( x ) - 2}{x ^{2}}

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

Solution steps

f^{'} (x) = - \frac{2 ( - 2 ln ( x ) - 1 )}{x ^{3}}

Find intervals:

Decreasing

: 0 < x < \frac{1}{e},

Increasing

: \frac{1}{e} < x < \infty

Plug

x = \frac{1}{e}

into

\frac{- 2 ln ( x ) - 2}{x ^{2}} : - e

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

f (x) = x^{2} + \frac{200}{x}, [0, \infty]

3 x^{2} - 6 x - 9, 0 \leq x \leq 4

\frac{( 1 - x ^{2} ) ^{3}}{x ^{3}}

121000 x - \frac{1000}{28} x^{2}

f (x) = - \frac{8}{3} x^{3} + 4 x^{2} + 48 x + 9

What is the extreme (-2ln(x)-2)/(x^2) ?
The extreme (-2ln(x)-2)/(x^2) is Minimum(1/(sqrt(e)),-e)