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Homework Help: Finding maximum curvature on lnx

  1. Dec 3, 2017 #1


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    Gold Member

    1. The problem statement, all variables and given/known data

    Determine the point on a plane curve f(x) = ln x where the curvature is maximum.

    2. Relevant equations

    k(x) = || T ' (x) || / || r ' (x ) ||

    k (x) = f '' (x) / [ 1 + ( f '' (x))2 ] 3/2

    3. The attempt at a solution

    f ' (x) = 1/x
    f " (x) = -1/x2

    k(x) = 1/x2 / { [1 + (1/x)2 ] 3/2 }

    k(x) = 1/x2 / { [ x2 +1 /x2 ] 3/2 }

    iirc we can use the first derivative and try to find the local max...but how do we even start it with this mess? quotient rule? Maybe there's something about the problem that tells us its impossible...? I'm lost here....
    Last edited: Dec 3, 2017
  2. jcsd
  3. Dec 3, 2017 #2


    Staff: Mentor

    There's a lot of extra stuff that I can't read in your formula above. What are these characters? ιι
    And what's this one? ι
    You lost a sign here (above).
    Sure, quotient rule would work, provided you are careful and methodical. It would be helpful to simplify the expression as much as possible for attempting to differentiate it.
  4. Dec 3, 2017 #3


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    Gold Member

    I cleaned it up a bit. Sorry!
  5. Dec 3, 2017 #4


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    Homework Helper

    There are some mistakes in your formulas.
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