Timeline for A question on decreasing function
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 8, 2016 at 20:08 | comment | added | Alex Degtyarev | Oops! Sorry. Then one of them is certainly true (probably, yours), and it seems sufficient to consider $f(t)=t$. | |
| Feb 8, 2016 at 19:10 | comment | added | Mark Fischler | Ah, but the problem states that all $a_i > 0$. So there will not be an extremum at any $x>0$. | |
| Feb 8, 2016 at 15:42 | comment | added | Alex Degtyarev | The conjecture is never true. Take your favorite polynomial p(x) with at least one extremum and let $f(t)=t$ or $-t$, whichever fits the conjecture. As is obvious from the graph, there would be both increasing and decreasing branches. One might be able to say something about the minimal/maximal root (and then, obviously, it suffices to consider the case $f(t)=\pm t$). | |
| Feb 8, 2016 at 15:35 | history | answered | Mark Fischler | CC BY-SA 3.0 |