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Homework Help: Prove that as a function of x, y never decreases

  1. Dec 5, 2016 #1
    1. The problem statement, all variables and given/known data
    y= A(x-sin(x)) with A as a constant.
    2. Relevant equations
    dy/dx = A(1-cos(x)) ??

    3. The attempt at a solution
    If I am thinking about this correctly, one can just differentiate the function as I have, and argue that when the gradient (dy/dx) is less than zero, the function is decreasing. So from this:

    so 1-cos(x)<0

    which never happens for any x, including negative x since cos is an even function.

    Is this the right way of doing this? I'm very rusty on proofs etc.

    Thanks in advance!
  2. jcsd
  3. Dec 5, 2016 #2


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    2017 Award

    Staff: Mentor

    That works, and you can prove it with the intermediate value theorem.
  4. Dec 5, 2016 #3
    Thank you very much indeed!
  5. Dec 5, 2016 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    Your conclusion is correct only if ##A >0##, which you did not state.
  6. Dec 5, 2016 #5
    Yeah sorry A is greater than zero, It's a combination of physical constants found earlier in the question.
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