Timeline for An inequality involving a polynomial and its first and second derivative
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2021 at 8:17 | comment | added | fedja | For 1a obviously no: take $P(x)=A+x^2-x^4$ with huge $A>0$ and shift it so that one of the roots is at the origin. | |
| Mar 8, 2021 at 23:16 | history | edited | JoshuaZ | CC BY-SA 4.0 |
Make version 1a of question 1, so isn't trivial.
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| Mar 8, 2021 at 23:14 | comment | added | JoshuaZ | @PietroMajer Thanks. That's a good point. So as written 1 is obviously false. Replacing 1 with some larger number solves that problem. I'll add a note. | |
| Mar 8, 2021 at 23:10 | comment | added | Pietro Majer | About Question 1: it may well happen that a polynomial $P(x)$ satisfies $P(0)= P'(1)=0$, $P(1)=1$ and $P''(1)=2$, say e.g. $P(x):=2x^3-5x^2+4x$. But then whatever is $f(n)$, for $x=1$ the rhs is smaller than the lhs. | |
| Mar 8, 2021 at 22:00 | history | asked | JoshuaZ | CC BY-SA 4.0 |