# when does this function grows and when it decreases?

• May 26th 2010, 04:10 AM
Ulysses
when does this function grows and when it decreases?
Hi there. I got this function, and I must find the intervals where it grows and when it decreases.

Here it is:

$f(x)=x\ln^2(x)$

I found its derivative:

$f'(x)=\ln^2(x)+2ln(x)$

From here I see that it will always grows when x>1. But, what happends before it gets to x=1? How must I think this problem?

Bye there, and thanks.
• May 26th 2010, 04:15 AM
drumist
You can factor the derivative, like so:

$f'(x) = \ln^2 x + 2 \ln x = (\ln x + 2) \ln x$

Now you can see that the extrema will occur when

$\ln x = 0$

or

$\ln x + 2 = 0$

Can you figure out the rest from here?
• May 26th 2010, 04:19 AM
Ulysses
I think I would. Thank you verymuch sir!