What is the extreme f(x)=-(e^{2x})/(-2x-5) ?

The extreme f(x)=-(e^{2x})/(-2x-5) is Minimum(-2, 1/(e^4))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=-(e^{2x})/(-2x-5)

extreme

Minimum (- 2, \frac{1}{e ^{4}})

Solution steps

f^{'} (x) = - \frac{- 4 e ^{2 x} x - 8 e ^{2 x}}{( - 2 x - 5 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - \frac{5}{2},

Decreasing

: - \frac{5}{2} < x < - 2,

Increasing

: - 2 < x < \infty

Plug

x = - 2

into

- \frac{e ^{2 x}}{- 2 x - 5} : \frac{1}{e ^{4}}

Minimum (- 2, \frac{1}{e ^{4}})

What is the extreme f(x)=-(e^{2x})/(-2x-5) ?
The extreme f(x)=-(e^{2x})/(-2x-5) is Minimum(-2, 1/(e^4))