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Math Help - when does this function grows and when it decreases?

  1. #1
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    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.
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  2. #2
    Senior Member
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    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?
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  3. #3
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    I think I would. Thank you verymuch sir!
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