
Re: counter example calculus
Posted:
Aug 4, 2013 2:43 PM


On Sunday, August 4, 2013 2:35:12 PM UTC4, Arturo Magidin wrote: > On Sunday, August 4, 2013 9:53:36 AM UTC5, G Patel wrote: > > > Is there a counter example to: > > > > > > > > > > > > "A function cannot be differentiable on a closed interval of its domain" > > > > > > (Note, I mean two sided, regular derivatives) > > > > 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). > > > > So what, exactly, do you mean? Or, what would "a counterexample" be? A function with *what precise properties*? >
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}

