MHB Is f(x)=ln(x)/x Increasing or Decreasing?

[Emma_011]

Find where increasing/decreasing, concavity, local extrema and inflection points for f(x)=ln/x

So here is what I have so far:

The derivative is 1-ln(x)/x^2

Critical points are (e,1/e)

No concavity

Local max is also (e,1/e) (no local min)

no inflection points

Increase on (0, e) and decrease on (e, positive infinity)

Is this correct? I tried to do a graph to justify my work

 

[I like Serena]

Find where increasing/decreasing, concavity, local extrema and inflection points for f(x)=ln x/x

The derivative is 1-ln(x)/x^2
Critical points are (e,1/e)
No concavity
Local max is also (e,1/e) (no local min)

Hi Emma, ☺

All correct so far.
Btw, how did you conclude that there is no concavity?

no inflection points

How did you reach that conclusion?
What is an inflection point exactly?

Increase on (0, e) and decrease on (e, positive infinity)

Correct.