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How to prove whether a function is differentiable

  1. Feb 10, 2014 #1
    1. The problem statement, all variables and given/known data

    Suppose that f is differentiable at x . Prove that ƒ(x)=lim[h→0] [itex]\frac{ƒ(x+h)-ƒ(x-h)}{2h}[/itex]

    2. Relevant equations



    3. The attempt at a solution
    I think that it may be proved by first principle,but I cannot rewrite the limit into the form of lim[h→0] [itex]\frac{ƒ(x+2h)-ƒ(x)}{2h}[/itex]
    So how can I solve this question?
    THANKS
     
  2. jcsd
  3. Feb 10, 2014 #2
    You probably mean f'(x). You can rewrite it via u = x-h.
     
  4. Feb 10, 2014 #3

    pasmith

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    I assume this is [itex]f'(x) = ...[/itex]

    Use [itex]f(x+h) - f(x-h) = (f(x+h) - f(x)) + (f(x) - f(x-h))[/itex]
     
  5. Feb 10, 2014 #4
    Sorry,but it maybe equals to 0.:confused:
     
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