What is the extreme s/(s^2+4s+5) ?

The extreme s/(s^2+4s+5) is Minimum(-sqrt(5),-(sqrt(5)+2)/2),Maximum(sqrt(5),(sqrt(5)-2)/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme s/(s^2+4s+5)

extreme

Minimum (- 5, - \frac{5 + 2}{2}), Maximum (5, \frac{5 - 2}{2})

Solution steps

f^{'} (s) = \frac{- s ^{2} + 5}{( s ^{2} + 4 s + 5 ) ^{2}}

Find intervals:

Decreasing

: - \infty < s < - 5,

Increasing

: - 5 < s < 5,

Decreasing

: 5 < s < \infty

Plug

s = - 5

into

\frac{s}{s ^{2} + 4 s + 5} : - \frac{5 + 2}{2}

Minimum (- 5, - \frac{5 + 2}{2})

Plug

s = 5

into

\frac{s}{s ^{2} + 4 s + 5} : \frac{5 - 2}{2}

Maximum (5, \frac{5 - 2}{2})

Minimum (- 5, - \frac{5 + 2}{2}), Maximum (5, \frac{5 - 2}{2})

What is the extreme s/(s^2+4s+5) ?
The extreme s/(s^2+4s+5) is Minimum(-sqrt(5),-(sqrt(5)+2)/2),Maximum(sqrt(5),(sqrt(5)-2)/2)