Mike the turd! (Was Ullrich the Mathematician!)

From: Jason (logamath_at_yahoo.com)
Date: 03/08/05 

Date: 8 Mar 2005 14:58:24 -0800

> Continuous differentiability on an open interval, together with
> continuity at the endpoints, does not buy you even one-sided
> differentiability at the endpoints. You can see this from
> a minor variation of the last example I posted. Let
>
> | x sin(1/x) , 0 < x <= 1
> f(x) = |
> | 0, , x = 0
>
> f is continuous at 0 and (continuously) differentiable on (0,1), but
not
> differentiable at 0.

Of course you are correct - you turd! But if you bothered reading
Gabriel's theorem, you would see that it requires the function to be
differentiable over [x;x+w) and continuous over [x;x+w].

Are there only fools on this forum?!

Jason

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