# Thread: critical numbers of x(lnx)^2

1. ## critical numbers of x(lnx)^2

I'm having trouble finding the critical numbers for the graph

$f(x)=x(lnx)^2$

I found the derivative

$f'(x)=2lnx + (lnx)^2$

From that I'm only seeing 1 as a critical number, and I know there is another. What is the thought process for solving the above equation when equal to zero?

2. Originally Posted by Shananay
I'm having trouble finding the critical numbers for the graph

$f(x)=x(lnx)^2$

I found the derivative

$f'(x)=2lnx + (lnx)^2$

From that I'm only seeing 1 as a critical number, and I know there is another. What is the thought process for solving the above equation when equal to zero?
$2ln(x)+\left(ln(x)\right)^2=0$.
$ln(x)[2+ln(x)]=0$.
$x=1,x=e^{-2}$.