Talk:Rolle's theorem

message: A number of contributors have "corrected" this section.  Before doing so, please stop and think about the theorem and whether it applies to functions with a vertical tangent.  Consider that the theorem can be applied (locally) to the inverse of the function.  That is, the theorem is more a geometric statement independent of coordinate system than one that depends on a particular coordinate system.
I will be the first to admit that the section could be worded better, and the notation [-\infty,+\infty] is non-standard.  Feel free to improve these.  However, please discuss technical changes here before making them to the article.  Thank you, Lunch 19:42, 15 April 2007 (UTC)
replies: text: A more standard notation is perhaps R. Thomas T Howard 03:11, 7 May 2007 (UTC)
thread_title: "Relaxed assumptions" and vertical tangents

message: The following is a description of my reasons for making the disputed edit on 19 November.
My intention was to introduce a more formal tone (as recommended in the style guide), and to remove the artificial sense of excitement and suspense from the existing text (which reads like and excerpt from a piece of advertising copy promoting a gripping weekend course which offers a unique insight into the fascinating history of mathematical analysis - a tale of deception, betrayal and human ambition, fraught with drama suspense from beginning to end).
My revision from:
 "A proof of the theorem had to wait until centuries later when ..."
to:
 "The first known formal proof of the theorem was offered by Michel Rolle in 1691 ..."
avoids patronising the reader by refraining from making unverifiable assertions. How can it possibly be proven that Rolle's proof was the very first one offered? The word known acknowledges this limitation. reetep (talk) 09:42, 20 November 2007 (UTC)
thread_title: Style in the History section

message: The third example exhibits the following function:
:
f(x)=\begin{cases}
\sqrt{1-x^2}&\text{for }x\in[0,1],\\
-\sqrt{1-x^2}&\text{for }x\in[-1,0].
\end{cases}
* This function is not well defined since it takes more than one value at zero.
* The assertion: "there is (even more than) one point in (−1,1) where the derivative is zero" is false.
* The description "two semicircles put together is a smooth way at the origin" is inaccurate. It is more like a quarter circle centred at the origin with radius r in the quadrant {x>0, y>0}, relected in the diagonal line y=-x, as illustrated below.
The function is a very interesting one, and very worthy of exhibition in this context. I'm just not sure that the function is suitable for making the point that the author intended. I will contact the author and see if they wish to amend the article according to his/her original intention, before diving in myself. reetep (talk) 11:43, 20 November 2007 (UTC)
replies: text: Sorry, I didn't shift the semicircles. Thank you for pointing this out. It should work now. Schmock (talk) 20:36, 20 November 2007 (UTC)

text: That is completely true - the given function is not differentiable on the interval, so the Rolle's theorem can not be applied. But you should have removed the reference of the third example as well. In the very next section, there is a mention of some third example (and there are only two), so I got confused, and had to search through history to find out what happened with that example :) -- Obradović Goran  (talk 02:01, 15 July 2008 (UTC)
thread_title: Third example

message: "Rolle's theorem essentially states that a smooth function [...]"
Seeing as smooth function has a precise meaning in mathematics other than just continuous function, maybe it would be better to change smooth to something else ?
Does anyone have any ideas ? -- Xedi (talk) 04:07, 22 February 2008 (UTC)
replies: text: Well, I think that differentiable is better term. I considered linking that to smooth function, but from the beginning of that article it is not clear what it means, and it means (in the context of Rolle's theorem) that function has first derivative. On the other hand, smooth is more intuitive, since a lot of people might not understand the concept of derivative. -- Obradović Goran  (talk 01:56, 15 July 2008 (UTC)
thread_title:  "Smooth" function 

message: How on earth can anyone say that the standard version of Rolle's theorem can fail, when, in fact, it doeas not; this is an implication, and if the antecedent does not hold, then how can anyone whine that neither the consequence does?! --84.47.117.130 (talk) 12:07, 3 January 2010 (UTC)
replies: text: I've restored a reworded version of the example. Paul August ☎ 19:34, 14 January 2010 (UTC)
thread_title:  Second example deleted 

message: I cannot find a reason for the arrow notation for the one-sided limits in the proof, especially when the statement used modern (0+ and 0-) notation. I shall change it.
Tebello TheWHAT!!?? 13:56, 14 January 2011 (UTC)
thread_title:  Quaint notation 

message: The history section incorrectly stated that Rolle proved the theorem, and did it using calculus. I've corrected it to this: "Although the theorem is named after Michel Rolle, Rolle's 1691 proof covered only the case of polynomial functions, and did not use the methods of differential calculus." More info: http://mathoverflow.net/questions/184358/what-did-rolle-prove-when-he-proved-rolles-theorem  — Preceding unsigned comment added by 76.169.116.244 (talk) 17:55, 21 June 2016 (UTC)
thread_title: fixed mistake in history

message: I wouldn't risk making an edit as all the participants seem more sophisticated in understanding than me.  I just have a question regarding this excerpt:
"As the induction hypothesis, assume the generalization is true for n − 1. We want to prove it for n > 1."
Souldn't that be changed to say
"As the induction hypothesis, assume the generalization is true for n − 1. We want to prove it for n = 1." — Preceding unsigned comment added by 2601:19B:C403:1D80:85D9:5E27:8EDC:8355 (talk) 20:44, 24 December 2019 (UTC)
replies: text: It was very awkwardly phrased, I have cleaned it up.  (Your proposed phrasing was completely wrong, but hopefully now it is clear.)  --JBL (talk) 15:45, 26 December 2019 (UTC)
thread_title: Question regarding this excerpt

message: Shouldn't this result by Rai & Van Ryzin be mentioned in the article? --bender235 (talk) 01:18, 29 May 2020 (UTC)
thread_title:  Multivariate version of Rolle's theorem