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Math Help - Determine whether or not the derivative exist

  1. #1
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    Determine whether or not the derivative exist

    Determine whether or not the derivative for the function f(x) below exists at x=0. Find f'(x) if exists.

    f(x) = { x^3 * cos (1/x) if x != 0

    { 0 if x = 0

    I'm sorry for being stupid. I personally think this problem is not hard
    And also I don't know how to do math code so forgive me

    Thank you in advance.
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  2. #2
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    |(f(x) - f(0)) / (x - 0)| = |f(x) / x| <= x^2, so f'(x) exists.
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