Tangencies for Power Functions with Integer Exponent
Year: 2025
Type: article
Abstract: Considering a power function f(x) = x^n with exponent n as a positive integer, we show that, at each of its points, there exists a unique polynomial function of degree n − 1 that is tangent to it at that point. Similarly, we verify that every power function h(x) = x^k with exponent k as a negative integer is tangent, at each of its points, to a function of the form l(x) =P t atxt, where the exponents t are integers between k + 1 and -1.
Source: Selecciones Matemáticas
Authors: Cairo Henrique Vaz Cotrim, Laredo Rennan Pereira Santos, Instituto Federal de Educacao, Ciencia e Tecnologia de Goías, Campus Formosa, Brasil.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4412771750