1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:

    A(1-cos(x))<0
    so 1-cos(x)<0

    cos(x)>1
    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

    mfb

    User Avatar
    2016 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

    User Avatar
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Prove that as a function of x, y never decreases
Loading...