Timeline for Non-negativity of a complicated function
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
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| Aug 15, 2023 at 15:21 | answer | added | River Li | timeline score: 0 | |
| Aug 13, 2023 at 13:21 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 13, 2023 at 10:06 | history | became hot network question | |||
| Aug 13, 2023 at 4:44 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 13, 2023 at 4:31 | vote | accept | japalmer | ||
| Aug 13, 2023 at 4:19 | answer | added | Iosif Pinelis | timeline score: 3 | |
| Aug 13, 2023 at 4:10 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 13, 2023 at 4:08 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 13, 2023 at 3:54 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 13, 2023 at 3:39 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 13, 2023 at 3:16 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 13, 2023 at 3:09 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 13, 2023 at 3:02 | comment | added | japalmer | @mathworker21 I updated the problem based on your response. | |
| Aug 13, 2023 at 3:01 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 13, 2023 at 2:53 | answer | added | user510394 | timeline score: 0 | |
| Aug 13, 2023 at 2:48 | comment | added | mathworker21 | I was just addressing your remark in the question: "but it is not monotonic". It sounded like the lack of monotonicity was a negative for you. And it could be that much cruder/dumber bounds work to establish the non-positivity of the derivative. | |
| Aug 13, 2023 at 2:45 | comment | added | japalmer | @mathworker21 Thanks, that looks like it works for $0 \le x \le 1/2$. But the monotonicity for $1/2 \le x \le 1$ (an inequality of the derivative) is back to a problem similar to original one isn't it? | |
| Aug 13, 2023 at 2:39 | comment | added | mathworker21 | For $0 \le x \le 1/2$, we have $5x^2-2 < 0$, so you can lower bound $f(x) \ge \arccos(1/2)^2+(36x^8-112x^6+93x^4-17x^2)$ on $0 \le x \le 1/2$. To then establish $f(x) \ge 0$ on $0 \le x \le 1/2$, it just suffices to show $36x^8-112x^6+93x^4-17x^2 > -1$ on $0 \le x \le 1/2$, which should be elementary enough (you can even drop the $36x^8$ term). And it appears, from Mathematica, that $f(x)$ is monotone decreasing on $1/2 \le x \le 1$. | |
| Aug 13, 2023 at 2:37 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 13, 2023 at 2:29 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 13, 2023 at 2:09 | comment | added | mathworker21 | Ha! I was going to recommend that exact edit to the title. | |
| Aug 13, 2023 at 2:08 | history | edited | japalmer | CC BY-SA 4.0 |
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| Aug 13, 2023 at 2:01 | history | asked | japalmer | CC BY-SA 4.0 |