Timeline for What does it mean to not be able to take the derivative of a function multiple times? [duplicate]
Current License: CC BY-SA 4.0
18 events
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| Jun 19, 2019 at 14:40 | comment | added | John Coleman |
@Peter I know what you meant and was just quibbling, but the point of the quibble is that "most functions" can be made rigorous in various ways, and when made rigorous your statement is likely false (depending on the class of functions and the definition of "most" chosen). For example, in the space of continuous functions on [0,1], the functions which are differentiable at even a single point comprise a meager set.
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| Jun 19, 2019 at 9:03 | comment | added | Peter | I mentioned the "pathological" functions. But I do not think the question is about all thinkable functions. | |
| Jun 19, 2019 at 8:36 | history | closed |
José Carlos Santos YuiTo Cheng Angina Seng Robert Soupe Cesareo |
Duplicate of Example of function that is differentiable, but the second derivative is not defined | |
| Jun 18, 2019 at 20:40 | review | Close votes | |||
| Jun 19, 2019 at 8:36 | |||||
| Jun 18, 2019 at 20:20 | comment | added | EJoshuaS - Stand with Ukraine | @JohnColeman It also depends on what your definition of "is" is. | |
| Jun 18, 2019 at 20:19 | comment | added | EJoshuaS - Stand with Ukraine | See here for an example of a function where the derivative of a function isn't differentiable. | |
| Jun 18, 2019 at 18:31 | comment | added | Bananach | @Peter Most mathematicians would say most functions are not differentiable at all | |
| Jun 18, 2019 at 18:07 | answer | added | Erdős-Bacon | timeline score: 7 | |
| Jun 18, 2019 at 17:21 | comment | added | John Coleman | @Peter Depends on what you mean by "most". | |
| Jun 18, 2019 at 15:35 | history | became hot network question | |||
| Jun 18, 2019 at 7:44 | comment | added | Peter | Most functions are differentiable infinite many times, at least in a suitable interval. Of course, one can construct "pathological" functions for nearly every property. Still a big class of functions are differentiable on $\mathbb R$ infinite many often, like the sine-function, the cosine-function, $e^x$ , the polynomials and any composition of those functions. | |
| Jun 18, 2019 at 7:41 | vote | accept | VictorVH | ||
| Jun 18, 2019 at 7:39 | answer | added | Henry | timeline score: 31 | |
| Jun 18, 2019 at 7:37 | answer | added | Sam Skywalker | timeline score: 10 | |
| Jun 18, 2019 at 7:37 | answer | added | alfba | timeline score: 7 | |
| S Jun 18, 2019 at 7:31 | history | suggested | Sam Skywalker | CC BY-SA 4.0 |
corrected arrow in f:I->R
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| Jun 18, 2019 at 7:28 | review | Suggested edits | |||
| S Jun 18, 2019 at 7:31 | |||||
| Jun 18, 2019 at 7:24 | history | asked | VictorVH | CC BY-SA 4.0 |