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Differantiation proof question

  1. Jan 20, 2009 #1
    if f(x) is differentiable on x_0
    prove that
    [​IMG]

    ??

    using the given i could
    say that lim [f(x+x_0) - f(x0)]/[x-x_0] exist
     
  2. jcsd
  3. Jan 20, 2009 #2

    quasar987

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    You sure could. But a little more to the point, you could say that

    [tex]f'(x_0)=\lim_{h\rightarrow 0}\frac{f(x_0+h)-f(x_0)}{h}=\lim_{h\rightarrow 0}\frac{f(x_0-h)-f(x_0)}{-h}[/tex]

    The rest is a judicious use of algebra.

    [Aren't you missing the limit sign and the "0" indices attached to the x's in you image?]
     
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