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On geometric forms for Cauchy’s and Flett’s mean value theorems
Sobre formas geométricas de los teorema del valor medio de Cauchy y de Flett
DOI:
https://doi.org/10.15446/bol.mat.v32n1.125632Palabras clave:
Cauchy’s mean value theorem, Flett’s theorem, Wachnicki’s theorem, differentiable curves (en)Teorema del valor medio de Cauchy, teorema de Flett, teorema de Wachnicki, curvas diferenciables (es)
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We give two mean value type theorems for differentiable curves in the Euclidean space. These unify several versions of Cauchy’s and Flett’s mean value theorems and provide equivalent geometric statements to their classical counterparts. We also discuss some particular cases for curves in two and three dimensions, and some related results
Presentamos dos teoremas del valor medio para curvas diferenciables en el espacio euclidiano. Estos unifican varias versiones de los teoremas del valor medio de Cauchy y Flett y proporcionan enunciados geométricos equivalentes a sus contrapartes clásicas. También analizamos algunos casos particulares para curvas en dos y tres dimensiones, y algunos resultados relacionados.
Referencias
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