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A simple extension of Rolle's theorem and its relation with multiple internal rates of return (IRR)

Author

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  • Fernando Gómez-Villaraga

Abstract

This paper presents a simple extension of Rolle's Theorem. This extension allows determining the amount of numbers ξ i in which f ' (ξ i ) = 0 in a given interval, using the characteristics of the function f in that interval. The extension has been proved, and the geometric interpretation has been presented. Illustrative examples have also been developed for each case that can be obtained by applying the extension. Finally, the study examines the relation of this theorem with the problem of multiple internal rates of return (IRR).

Suggested Citation

  • Fernando Gómez-Villaraga, 2019. "A simple extension of Rolle's theorem and its relation with multiple internal rates of return (IRR)," Revista Finanzas y Politica Economica, Universidad Católica de Colombia, vol. 11(2), pages 241-258, November.
    • Handle: RePEc:col:000443:018467
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    File URL: https://revfinypolecon.ucatolica.edu.co/article/view/2376
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    More about this item

    Keywords

    Multiple internal rates of return (IRR); Rolle's theorem.;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • G00 - Financial Economics - - General - - - General

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