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Math Help - critical numbers of x(lnx)^2

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by Shananay View Post
    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}.
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