Tangencies for Power Functions with Integer Exponent

• Autores: Vaz Cotrim, Cairo Henrique, Pereira Santos, Laredo Rennan
• Formato: artículo
• Fecha de Publicación: 2025
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: portugués
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/6637
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6637
• Nivel de acceso: acceso abierto
• Materia: Funcoes Potencia; Tangencia; Teorema Binomial; Power Function; Tangency; Binomial Theorem

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) =Sa^t.x^t, where the exponents t are integers between k + 1 and −1.