Re: f continuous on [a,b] and differentiable on (a,b)-


G. A. Edgar wrote:
> > >
> > >My question is really why the endpoints are not included for the
> > >differentiable hypothesis. Aren't functions that are continous on
> > >[a,b] and differentiable on (a,b) also differentiable from one side at
> > >the endpoints?
>
> No. Probably if you think about it you can find a counterexample
> yourself.
>

Thanks all, now I understand why the endpoints are not included for
differentiability.

One other question. It goes without saying that if a function if
differentiable on (a,b) it must be continuous on [a,b]. So why do
theorems like Mean Value state the continous hypothesis separately?

.

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