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Homework Help: I need a function

  1. Nov 30, 2004 #1

    I am looking for a non-linear function f(x) such that f'(x1) = f'(x2) but x1 != x2.

  2. jcsd
  3. Nov 30, 2004 #2
    I guess sin(x) will do... :)
  4. Nov 30, 2004 #3
    Although I wouldn't mind hearing other suggestions, I'm sure there are lots of functions that satisfy this requirement.

  5. Nov 30, 2004 #4


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    Any function that is not injective has the quality that f(x_1) = f(x_2) does not imply that x_1 = x_2.

    edited to add: oops I see he little ' now,, in this case you just need it so the derivative of the function is not injective.

    So quickly f'(x) = 3x^2 is not injective and f(x) = x^3 is non-linear.
    Last edited: Nov 30, 2004
  6. Nov 30, 2004 #5


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    Here's a couple :
    1) any periodic function,
    2) any polynomial higher than a quadratic
  7. Dec 1, 2004 #6
    Hmm, sorry I think I forgot to mention one thing. I tried to simplify the task, which is to find a non-linear function, so that its tangent line at (x1, f(x1)) is the same tangent line at (x2, f(x2)). So in that perspective, x^3 doesn't work.

    Thanks :)
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