Do derivatives always exist in a neighborhood?

slamminsammya · Sep 21, 2010

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] ?

JG89 · Sep 21, 2010

I asked the same question as you before:

https://www.physicsforums.com/showthread.php?t=306278

The answer is no.

Do derivatives always exist in a neighborhood?

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Do derivatives always exist in a neighborhood?

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