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Do derivatives always exist in a neighborhood?

  1. Sep 21, 2010 #1
    Suppose that [tex]f:\mathbb{R} \to \mathbb{R}[/tex] is continuous and [tex]f'(x_0)[/tex] exists for some [tex]x_0[/tex] . Does it follow that [tex]f'[/tex] exists for all [tex]x[/tex] such that [tex]|x-x_0|<r[/tex] for some [tex]r>0[/tex] ?
  2. jcsd
  3. Sep 21, 2010 #2
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