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Homework Help: Making a piecewise defined function differentiable

  1. Oct 16, 2007 #1
    I have to find the values of a and b in terms of c so that this function is differentiable. Attached is the problem and my work, but I think that there's an error somewhere in my attempt. Any advice?
     

    Attached Files:

  2. jcsd
  3. Oct 16, 2007 #2

    Dick

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    Yes, check your derivative of 1/|x| at x=c. It's not zero. You made an algebraic mistake.
     
  4. Oct 16, 2007 #3
    I see I forgot to distribute a negative sign on the left side's derivative, but that's trivial, because as h-->0, (-h) and (h) both approach 0.

    Is there something else I'm missing? I've re-done the rest of the algebra, and I'm still getting 0.

    EDIT: I see what went wrong. I moved the h up to the top of the fraction, instead of keeping it on the bottom.
     
    Last edited: Oct 16, 2007
  5. Oct 16, 2007 #4
    I think I've solved it (see attached). My only concern is that I've ignored the absolute value signs. Is this a problem? Or should I go back and work it through with two cases, one when X>0 or equal to 0 and one when X<0?

    That seems to me the better way, but I'm wondering if it's necessary?
     

    Attached Files:

  6. Oct 16, 2007 #5

    Dick

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    You posted an attachment, so I can't see it yet, but yes, you should probably do two cases. That's kind of what absolute values are all about.
     
  7. Oct 17, 2007 #6

    HallsofIvy

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    Since f(x)= 1/|x| only for |x|> C for some positive number C, the derivative of 1/|x| at x=0 doesn't matter (fortunately)! What is crucial is the value and derivative of 1/|x| at x= C and x= -C.
     
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