Timeline for kth finite difference always positive when kth derivative is?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Oct 23, 2016 at 17:00 | review | Close votes | |||
| Oct 23, 2016 at 17:45 | |||||
| Oct 23, 2016 at 2:09 | comment | added | George Shakan | @NateEldredge Yes of course, I tried to be more clear. I've never seen $f > 0$ mean there exists an x such that $f(x) >0$, so that interpretation wasn't on my radar. | |
| Oct 23, 2016 at 2:07 | history | edited | George Shakan | CC BY-SA 3.0 |
added 59 characters in body
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| Oct 22, 2016 at 19:59 | comment | added | Nate Eldredge | So, there are incompatible answers based on different interpretations of the question. I read it as asking that the function be $k$ times differentiable on all of $\mathbb{R}$, and the $k$th derivative strictly positive everywhere. Zak, can you edit the question to clarify what you want? Also, the expression $\Delta(g,h)$ defines a function of $x$, if I read it correctly. Are you asking whether $\Delta(f, h_1, \dots, h_k)(x) > 0$ for all $x$, some $x$, etc? And for every $h_1, \dots, h_k > 0$? | |
| Oct 22, 2016 at 18:49 | vote | accept | George Shakan | ||
| Oct 22, 2016 at 18:43 | vote | accept | George Shakan | ||
| Oct 22, 2016 at 18:45 | |||||
| Oct 22, 2016 at 18:43 | comment | added | Anixx | Strictly positive for all x is the first example in my answer. | |
| Oct 22, 2016 at 18:41 | vote | accept | George Shakan | ||
| Oct 22, 2016 at 18:43 | |||||
| Oct 22, 2016 at 18:32 | comment | added | Anixx | For function $f(x)=10 (1 - \exp(-1/(x + 0.1)^2)) - 9) + \exp(x)$ first 13 derivatives at zero are positive, while the first difference is negative. See my answer. | |
| Oct 22, 2016 at 18:19 | vote | accept | George Shakan | ||
| Oct 22, 2016 at 18:41 | |||||
| Oct 22, 2016 at 18:17 | vote | accept | George Shakan | ||
| Oct 22, 2016 at 18:19 | |||||
| Oct 22, 2016 at 17:59 | answer | added | Anixx | timeline score: 1 | |
| Oct 22, 2016 at 17:53 | answer | added | Fedor Petrov | timeline score: 6 | |
| Oct 22, 2016 at 17:46 | history | asked | George Shakan | CC BY-SA 3.0 |