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Finding the X-intercept of a function

  1. Nov 29, 2014 #1
    1. The problem statement, all variables and given/known data
    F(x)= x-12x1/3 Find the X-intercept

    2. Relevant equations
    X-intercept means y=0

    3. The attempt at a solution
    My math teacher gave plus or minus 24sqrt3 as an answer, but I have no idea how he got that! He also got 0, but I do understand that one... I just don't know how to get the 24sqrt3 Could someone help me, please?
     
  2. jcsd
  3. Nov 29, 2014 #2

    Ray Vickson

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    Set ##u = x^{1/3}##, so your equation becomes ##0 = u^3 - 12 u##, or ##0 = u(u^2-12)##.
     
  4. Nov 29, 2014 #3
    Thank You! Quick question: since you put everything to the cube, should you put -12 also to the power three, because that's how I finally got the answer! Thank you so much!!!
     
  5. Nov 29, 2014 #4

    RUber

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    The u-substitution is all you need. However, the answer you get is for u. x = u^3. So you will cube your answer.
    There should be no reason to cube 12. That would be assuming that
    ##F(x)^3=(x-12x^{1/3})^3 = x^3 - 12^3 x## but that is not how powers of polynomials work.
    Edit:
    However, in this case, since you are assuming that F(x) = 0 (x- intercept), you will get the right solution since:
    ##0=x-12x^{1/3}##
    ##x=12x^{1/3}##
    ##x^3=12^3x##
    ##0=x^3-12^3x##
    There are many ways to get to the answer...just be sure you know why you are doing things.
     
    Last edited: Nov 29, 2014
  6. Nov 30, 2014 #5
    Thank you so much! This community really is awesome!
     
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