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Homework Help: Finding the point of inflection of the integral of (sin(x))/x

  1. Sep 28, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the coordinates of the first inflection point to the right of the origin.


    2. Relevant equations



    3. The attempt at a solution
    I know that the inflection point would equal zero for the second derivative of a function and that the second derivative of this function is (xcosx-sinx)/x².
    (xcosx-sinx)/x² = 0
    (xcosx-sinx) = 0
    xcosx = sinx
    x = tanx

    I'm not sure what to do after this or if the steps were taken incorrectly.
     
  2. jcsd
  3. Sep 28, 2010 #2
    I don't see what's wrong with that unless you don't know how to then find them numerically.
     
  4. Sep 28, 2010 #3
    I know that I can find the approximate number but I don't know where to go next to find the exact value of x for the first inflection point.

    I don't know what steps to take next to isolate x in one side and to have one x.
     
  5. Sep 28, 2010 #4
  6. Sep 28, 2010 #5
    So then an acceptable answer would be (tan(x),Si(tan(x))?
     
  7. Sep 28, 2010 #6
    The points of inflexions are when [tex] \tan x = x [/tex] as you said. This equation have an infinite number of solutions.

    I don't really understand what you mean with [tex] ( \tan(x), Si(\tan(x) ) [/tex].
    One point of inflexion would be for example [tex] ( x_1 , Si(x_1))[/tex] where [tex]x_1[/tex] is defined to be the first positive solution to the equation [tex] \tan x = x [/tex]
     
  8. Sep 28, 2010 #7
    I see and understand now. Thanks for the help.
     
  9. Sep 28, 2010 #8
    [EDIT] Thanks Inferior89

    [STRIKE]Actually that's just the first derivative, not the second.
    [/STRIKE]
    If you want to [STRIKE]consider the values that give the extreme points of sinx/x where you would actually[/STRIKE] solve x = tanx, you might want to take a look here on the second page.
    http://press.princeton.edu/books/maor/chapter_10.pdf [Broken]
    Very interesting. :smile:
     
    Last edited by a moderator: May 4, 2017
  10. Sep 28, 2010 #9
    He is finding the second derivative of Si(x) not sin(x)/x.
     
    Last edited by a moderator: May 4, 2017
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