|WikiProject Mathematics||(Rated B-class, High-importance)|
A picture would be much wanted to show the points of minimum, the points of maximum, and the inflection points. Oleg Alexandrov 13:05, 23 December 2004 (UTC)
- Agreed. I added said pics, what do you think ? StuRat 22:56, 27 August 2005 (UTC)
First paragraph of articles states "An equivalent definition is where the derivative of the function equals zero (known as a critical number)."
This suggests: f'(c) = 0 <==> c is a critical number, which is not true (reverse is not true)
What about linked extremums? --Čikić Dragan 13:42, 13 March 2006 (UTC)
There really should be a comment about the use of the term in Astronomy. CFLeon 23:31, 17 May 2006 (UTC)
- Such as ? StuRat 05:06, 18 May 2006 (UTC)
- When the Earth passes an outer planet, it appears to stop and then reverse for awhile, then stop and go the first way. Those are called the stationary points of an orbit. CFLeon 22:37, 18 May 2006 (UTC)
Section 3.1 "Example" begins by discussing f' and points x1, x2, etc. with no mention of f or a picture or definition of the points. Is a picture missing? Thanks. EJR 19:37, 17 June 2007 (UTC)
Anyone else agree this is confusing?
The first sentence in the current version is:
"a stationary point is an input to a function where the derivative is zero (equivalently, the gradient is zero): where the function "stops" increasing or decreasing (hence the name)."
But the function doesn't stop increasing or decreasing if the stationary point is an inflection point. Perhaps the sentence should be amended to be "...the DERIVATIVE of the function stops increasing or decreasing (hence the name)."
Critical vs. stationary
I have modified the lead to clarify the difference between stationary point and critical point, in order to follow the terminology of differential geometry, which is the standard for this question. Nevertheless, the remainder of the article needs to be rewritten and sourced in accordance with this edit.
By the way, above post on stationary points in astronomy is a good illustration of the subject: these stationary points are exactly the critical points of the projection of the orbit of a planet on the celestial sphere.