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Maximum - Can this be solved algebraically?

  1. Jan 15, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the absolute extrema of f(x) = e^-x * ln(lnx)

    3. The attempt at a solution
    Ive successfully taken the first derivative and set it to zero. The problem is checking the sign of 1/(xlnx) - ln(lnx)

    No matter how I try to manipulate this, I cant seem to isolate x. Its clear with a graphing calculator that f' changes from positive to negative at about 3.5, but this is supposed to be done without a graphing utility (if I could use one in my answer, I might as well have found the maximum from the start by graphing). Can this be set to zero and solved without a calculator?

    Other forms include
    1 - x*lnx*ln(lnx) = 0
    lnx^(xlnx) - e = 0
  2. jcsd
  3. Jan 15, 2008 #2


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    Science Advisor
    Homework Helper

    No, I don't think you can solve that without using numerical methods, such as a graphing calculator.
  4. Jan 17, 2008 #3
    I found out today that we were supposed to use Newtons Method with a scientific calculator
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