On the remainder in the Taylor theorem

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213366We give a short straightforward proof for the bound of the reminder term in the Taylor theorem. The proof uses only induction and the fact that $f'\geq 0$ implies the monotonicity of $f$, so it might be an attractive proof to give to undergraduate students.2 pages, the proof was shortenedClassical Analysis and ODEs26A24On the remainder in the Taylor theoremtext