Question

find the intervals in which the function f(x)=logx/x increasing or decreasing.
​​

Answer 1

I hope this attachment will help you.

Answer 2

Answer:

Given : The function $f(x)=\frac{\log x}{x}$

To find : The intervals in which the function is increasing or decreasing.

Solution :

To find the increasing, decreasing we find the derivative.

$f(x)=\frac{\log x}{x}$

$f'(x)=\frac{x\times \frac{1}{x}-\log x}{x^2}$

$f'(x)=\frac{1-\log x}{x^2}$

Now, to find terminating points put f'(x)=0

$\frac{1-\log x}{x^2}=0$

$1-\log x=0$

$\log x=1$

$x=e$

The function is

Increasing on:  (0,2.71828184)

Decreasing on : (2.71828184,∞)

Refer the attached figure.