What is the monotone f(x)=e^x-e^{3x} ?

The monotone f(x)=e^x-e^{3x} is Increasing:-infinity <x<-1/2 ln(3),Decreasing:-1/2 ln(3)<x<infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

monotone f(x)=e^x-e^{3x}

monotone

Increasing : - \infty < x < - \frac{1}{2} ln (3), Decreasing : - \frac{1}{2} ln (3) < x < \infty

Solution steps

f^{'} (x) = e^{x} - e^{3 x} \cdot 3

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2} ln (3),

Decreasing

: - \frac{1}{2} ln (3) < x < \infty

Increasing : - \infty < x < - \frac{1}{2} ln (3), Decreasing : - \frac{1}{2} ln (3) < x < \infty

What is the monotone f(x)=e^x-e^{3x} ?
The monotone f(x)=e^x-e^{3x} is Increasing:-infinity <x<-1/2 ln(3),Decreasing:-1/2 ln(3)<x<infinity