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Topic: Some derivative/continuity questions
Replies: 15   Last Post: Aug 5, 2013 9:47 AM

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Leon Aigret

Posts: 31
Registered: 12/2/12
Re: Some derivative/continuity questions
Posted: Aug 3, 2013 8:11 PM
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On Sat, 3 Aug 2013 13:37:09 -0700 (PDT), G Patel
<gaya.patel@gmail.com> wrote:

>1) If f is differentiable at x, is it continuous on an interval about x?
>It seems intuitively like it should be.
>
>2) Do you know a function that is differentiable at an isolated point?


Combining ideas from this thread:

f defined by f(x) = 0 for rational x and fx) = 1 for irrational x is
not continuous anywhere, but x^2 f(x) is continuous and differentible
in only one point.

Leon



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