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Subject: Re: Problem
Date: Thu, 6 May 2010 08:15:14 +0000 (UTC)
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"Roger Stafford" <> wrote in message <hrt7e0$drs$>...
>   Prepare yourself for a long-winded explanation. .......
- - - - - - - - -
  Please add this onto the previous discussion I gave.

  If y = f(x) is some continuous function with its first three derivatives also continuous over the interval xa < xb < xc, then by an extension of the famous Rolle's theorem of elementary calculus, there is a value xi (Greek letter) such that the difference between the expression above for an approximation of the derivative at xb and the actual derivative, f'(xb) is equal to


where xi lies in xa < xi < xc and f'''(xi) is the third derivative value of f(x) there.  A remarkable fact!

  What this signifies is that if the function whose derivative you are attempting to approximate with the formula I gave you has a third derivative which remains very small - in other words is reasonably smooth - then you are guaranteed a close approximation.

Roger Stafford