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Homework Help: Find all the critical points of the function

  1. May 22, 2013 #1
    The problem statement, all variables and given/known data

    f(x) = x ln(x)

    The attempt at a solution

    f'(x) = product rule, resulting in 1 + ln (x)

    So by way of solving the problem, set 1 + ln (x) = 0

    Now idealistically, find something in x that, when added to 1, equals zero.

    Now here's a problem I have. How do I know when to keep searching for something in ln (x) and when to subtract one on both sides to make ln (x) = 1 ? And even when I get to that point, how to I move forward?
  2. jcsd
  3. May 22, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    I'm not sure why you are so confused. You want to solve log(x)=(-1). Exponentiate both sides.
  4. May 22, 2013 #3


    Staff: Mentor

    Add -1 to both sides to get ln(x) = -1
    Now solve for x.
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