Timeline for polynomials with similar maxima-minima
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2015 at 16:41 | comment | added | Yaakov Baruch | @alpx $(x^{2m}+y^{2m})/(x^2+y^2)^m$ has absolute max points at $(\pm 1, 0), (0, \pm 1)$ and absolute min points at $(\pm \frac{\sqrt{2}}{2}, \pm \frac{\sqrt{2}}{2})$. These are then max/min points on $S^1$ too since $x^2+y^2$ is 1 there. Raising to odd powers then only changes the values, not the locations, of extreme points. I think similar result hold in higher dimensions too. | |
| Mar 19, 2015 at 15:40 | comment | added | alpx | @ Yaakov: Thanks for the answer. Could you please explain a little about your computations? Otherwise one could still write a generic algebraic relation with this polynomials. | |
| Mar 18, 2015 at 14:30 | history | answered | Yaakov Baruch | CC BY-SA 3.0 |