Horizontal chords of the graph of a continuous function
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- by Uwe Herzberg
- Proc. Amer. Math. Soc. 49 (1975), 179-184
- DOI: https://doi.org/10.1090/S0002-9939-1975-0357701-9
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Abstract:
The continuous function $f$, defined on $[a,b]$, changing sign exactly $n$ times on $(a,b)$, and $f(a) = f(b) = 0$, has horizontal chords of every length $h < H$ with endpoints in $(a,b)$. We determine the largest such $H$ as a function of $n$.References
- R. J. Levit, The finite difference extension of Rolle’s theorem, Amer. Math. Monthly 70 (1963), 26–30. MR 147592, DOI 10.2307/2312779
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 49 (1975), 179-184
- MSC: Primary 26A15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0357701-9
- MathSciNet review: 0357701