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Derivative and continuity

  1. Apr 26, 2013 #1
    1. The problem statement, all variables and given/known data

    I have this problem I haven been trying to solve for a while:

    "Check if the following function is continuous and/or differentiable :"

    / (x^2-1) /2 , |x|=< 1
    f(x) = \ |x| -1 , |x| > 1

    3. The attempt at a solution

    So I managed to prove it is continuous for all x by checking the limits as x -> 1 from both directions = 0
    and the limit as x -> 0 from both directions = -1/2 (is that necessary?)
    from that point it's continuous for all x as a polynomial in either branch.

    is that correct so far?

    now the problem starts with the derivative check...

    I get that the f'(x) = x , |x| < 1
    or f'(x) = x/|x| , |x| > 1

    so does that alone means the function isn't differentiable in x = 0 ?

    Thank you for your help!
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Apr 26, 2013 #2


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    Science Advisor
    Homework Helper
    Gold Member

    You also need to check at x = -1
    No. It is a polynomial there.
    There is no problem at x=0. The problem is at x = 1 and -1 where the two functions piece together. You need to check the function values and slopes there.
  4. Apr 26, 2013 #3
    THANKS a lot you helped me solved this at last!
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