Illumination by Taylor Polynomials
| dc.creator | Horwitz, Alan | |
| dc.date | 1999-08-19 | |
| dc.date | 2002-06-17 | |
| dc.date.accessioned | 2026-07-07T05:30:24Z | |
| dc.date.available | 2026-07-07T05:30:24Z | |
| dc.description | Let f(x) be a differentiable function on the real line R, and let P be a point not on the graph of f(x). Define the illumination index of P to be the number of distinct tangents to the graph of f which pass thru P. We prove that if f '' is continuous and nonnegative on R, f '' > m >0 outside a closed interval of R, and f '' has finitely many zeroes on R, then every point below the graph of f has illumination index 2. This result fails in general if f '' is not bounded away from 0 on R. Also, if f '' has finitely many zeroes and f '' is not nonnnegative on R, then some point below the graph has illumination index not equal to 2. Finally, we generalize our results to illumination by odd order Taylor polynomials. | |
| dc.description | Minor modifications and corrections | |
| dc.identifier | https://arxiv.org/abs/math/9908100 | |
| dc.identifier | http://arxiv.org/abs/math/9908100 | |
| dc.identifier | International Journal of Mathematics and Mathematical Sciences 27(2001), 125-130 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78978 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 26A06 | |
| dc.title | Illumination by Taylor Polynomials | |
| dc.type | text |