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Re: counter example calculus
Posted:
Aug 4, 2013 2:43 PM
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On Sunday, August 4, 2013 2:35:12 PM UTC-4, Arturo Magidin wrote:
> On Sunday, August 4, 2013 9:53:36 AM UTC-5, G Patel wrote:
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> > Is there a counter example to:
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> > "A function cannot be differentiable on a closed interval of its domain"
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> > (Note, I mean two sided, regular derivatives)
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> This is unclear to me. To me, a counterexample to this statement would be a function f whose domain includes a closed interval [a,b] such that f' exists on all points of [a,b]. But this is trivial (e.g., a constant function).
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> So what, exactly, do you mean? Or, what would "a counterexample" be? A function with *what precise properties*?
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Ok I have to refine my question (it was incorrectly stated). Sorry.
: Is there a function that is DEFINED on an interval that extends a closed interval [a,b] both on its left and right, where the function is differentiable on [a,b] but not on the extensions.
: How about if I change DEFINED to CONTINUOUS?
{My line of thinking is that it would be hard to find these examples because the derivative is a two sided limit}
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