when does this function grows and when it decreases?

May 2010
254
8
Hi there. I got this function, and I must find the intervals where it grows and when it decreases.

Here it is:

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

I found its derivative:

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

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.
 
Jan 2010
354
173
You can factor the derivative, like so:

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

Now you can see that the extrema will occur when

\(\displaystyle \ln x = 0\)

or

\(\displaystyle \ln x + 2 = 0\)

Can you figure out the rest from here?
 
  • Like
Reactions: Ulysses
May 2010
254
8
I think I would. Thank you verymuch sir!