Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: Problem Date: Thu, 6 May 2010 08:15:14 +0000 (UTC) Organization: The MathWorks, Inc. Lines: 14 Message-ID: <hrttqi$ftj$1@fred.mathworks.com> References: <hrqe77$jcs$1@fred.mathworks.com> <1317322228.78895.1273096933766.JavaMail.root@gallium.mathforum.org> <hrt7e0$drs$1@fred.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: webapp-03-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: fred.mathworks.com 1273133714 16307 172.30.248.38 (6 May 2010 08:15:14 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Thu, 6 May 2010 08:15:14 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 1187260 Xref: news.mathworks.com comp.soft-sys.matlab:633055 "Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <hrt7e0$drs$1@fred.mathworks.com>... > 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 1/6*f'''(xi)*(xc-xb)*(xb-xa) 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