Talk:Concave function

message: This page states that a twice-differentiable function is concave if and only if (iff) the second derivative is negative. I don't think this is correct.
A twice-differentiable function is STRICT concave if and only if the second derivative is negative.
Use a constant function as an example. By the simpler definition, a constant function (or a linear function) is always concave (but not strictly concave). However, the second derivative is ZERO, not negative.
:You are right; I corrected the text. --NeoUrfahraner 14:17, 1 Mar 2005 (UTC)
replies: text:  But what about; A differentiable function f is concave on an interval if and only if its derivative function f ′ is monotonically decreasing on that interval, that is, f<0: a concave function has a decreasing slope.Shouldn't this be f\leq 0 too (+ the slope can be constant)?  — Preceding unsigned comment added by Bgst (talk • contribs) 18:16, 23 August 2017 (UTC)
replies: text:  I agree. I just changed it accordingly. Does it look better now? Yak90 (talk) 16:14, 10 October 2017 (UTC)

text: OK, corrected again --NeoUrfahraner 11:14, 2 Mar 2005 (UTC)
thread_title: ?

message: Merging looks like a good idea to me, but one should merge this article in convex function and not viceversa I think. Also, convex function looks like a rather well-written article, so hopefully the merged version will not be worse than what it is now. In short, if anybody is willing to merge, that person should be willing to take the necessary time to do a good job. Otherwise I would oppose a merger. Oleg Alexandrov (talk) 12:12, 24 October 2005 (UTC)
replies: text: See also Talk:Convex function. Oleg Alexandrov (talk) 00:29, 30 December 2005 (UTC)
thread_title:  Merging with [[convex function]]? 

message: "The definitions of convex and concave functions given here appear to be incorrect.  What is said to be a concave function is a convex function and what is said to be a convex function is a concave function. 
I have always found those terms confusing.  The Chinese characters for the two terms have the shapes that they describe, so it is easy to recognise.  The charactor for convex (or concave downward) is a protrusion on top of a square, and the one for concave (or concave upward) is a depression on the top side of a square."
Sorry it seems that I posted the above by mistake.  I pressed "Save" and did not realise that my comment is already posted.  I did not mean to edit the page but only wanted to ask the author the page to check carefully.  I have not learned how to delete the paragraphs I added at the end of the item, which look ugly.  Could you delete them?  Please check your definitions.
Ziheng Yang
: Would you mind making an account if you would like to contribute more? It is better to keep in touch that way. 
: As far as I can tell, everything is correct. Concave up is the same as convex, meanining a function of this form" \_/
: Concave down is the same as concave, meaning a function of this form: 
   ----
  /    \
 /      \
: Other comments? Oleg Alexandrov (talk) 18:27, 30 December 2005 (UTC)
replies: text: (Ziheng Yang) It is the Chinese knowledge that makes you misunderstand. As a native Chinese speaker, I used to have the same misunderstanding too. The English term are not exactly the same as the Chinese term. The English term "concave" means "curving in", but the Chinese term 凹 primarily means "lower than the ground" and secondarily means "curving in". The English term "convex" means "curving out", but the Chinese term 凸 primarily means "higher than the ground" and secondarily means "curving out". When we see the English term "concave function" and translate it into Chinese 凹函数, we usually take the primary meaning in Chinese so the literal meaning seems to be the "function lower than the ground", like this \/, but it really does not mean this in English. The English term literally means the function curving in (relative to the upper area of the function curve), so it should look like this /\. --Yejianfei (talk) 12:23, 2 March 2020 (UTC)
thread_title: Incorrect definition?

message: "Equivalently, f(x) is concave on [a, b] if and only if the function −f(x) is convex on every subinterval of [a, b]."
I feel like this line might be glomming together two separate points. Are both of the following correct?:
1) A function f is concave an [a,b] iff -f is convex on [a,b].
2) A function f is concave (convex) on [a,b] iff it is concave (convex) on every /proper/ (was this word left out of the original?--it makes the statement less trivial) subinterval of [a,b].
If these are both true, maybe they should replace the current language. Also, the placement of this part suggests that the statement is restricted to continuous functions. Is that desired? --Dchudz 15:48, 25 July 2006 (UTC)
replies: text: That is right, I think it should read "Equivalently, f(x) is concave on [a, b] if and only if the function −f(x) is convex on [a, b]"--A 19:24, 13 October 2007 (UTC)
thread_title: Convex on every subinterval

message: The current definition uses a concave set. This makes no sense. Both convex and concave functions are defined over CONVEX sets. I'm going to change it to a convex set. 
http://www.chass.utoronto.ca/~osborne/MathTutorial/CVN.HTM
--TedPavlic 17:44, 11 May 2007 (UTC)
replies: text: 69.140.152.55 (talk) 16:28, 19 May 2008 (UTC)

text: I have removed the  tag, as the article now meets WP:MTAA. Gandalf61 (talk) 16:06, 13 August 2008 (UTC)
thread_title: Convex and Concave Sets

message: This article could benefit from a few simple examples.
zermalo (talk) 18:29, 20 May 2008 (UTC)
replies: text: I added a few. Oleg Alexandrov (talk) 04:02, 21 May 2008 (UTC)
thread_title:  Examples ? 

message: A graph, similar to the one for Convex function would be useful here.  —Preceding unsigned comment added by Nandhp (talk • contribs) 15:14, 2 November 2008 (UTC)
thread_title:  Diagram request 

message: I noticed that when viewed in Safari on my iPhone, the definition of concavity shows up incorrectly: the term \alpha f(y) does not appear. The page looks fine in multiple browsers on my laptop, and I don't see what could be causing the problem.Danramras (talk) 22:34, 6 September 2017 (UTC)
thread_title:  Display error on mobile page 

message: Please explain the history of this term, and why such graphs are called "concave" (viewed from below) and not "convex" (viewed from above). 
—DIV (120.17.118.20 (talk) 13:31, 8 October 2018 (UTC)
thread_title:  Nomenclature 

message: Pretty sure the equations in the definition section are wrong. Leopd (talk) 08:16, 31 January 2021 (UTC)
thread_title:  Equations <ins>appear</ins> wrong <ins>in iOS</ins> in definition