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Homework Help: Finding the point of inflection for the function

  1. Feb 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Find any points of inflection for the function y = x - cos x on the interval {0,2pi}

    2. Relevant equations

    3. The attempt at a solution

    Well i know the second derivative is cos x, and I know it equals 0. But im just not sure what to give as a final answer. cos x = 0 at pi/2 and 3pi/2 but is that the final answer?

    Thank you for your help!
  2. jcsd
  3. Feb 26, 2009 #2


    Staff: Mentor

    cos(x) is not identically zero. To confirm that there are inflection points for x = pi/2 and x = 3pi/2, check to see whether the concavity changes around these values. IOW, does y'' change sign at pi/2 and 3pi/2? If so, you're almost done, and the only other thing is to find the y values at these points. Those will be your inflection points.
  4. Feb 26, 2009 #3
    how do I check around those values, Im not sure how to use something like pi/2 in this case.
  5. Feb 26, 2009 #4


    User Avatar
    Science Advisor

    Then use pi/2+ .001 and pi/ - .001! What do you mean "use pi/2"? It is a number! enter it into your calculator. Be sure you calculator is set to "radian" mode of course.
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