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Extensions of
Rolle's theorem
Laura J. Batts, Megan E. Moran and Courtney K. Taylor
Vol. 15 (2022), No. 4, 641–648
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Abstract |
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Repeatedly differentiating a polynomial with distinct real roots and then finding the roots of each derivative produces a sequence of real numbers. The classical Rolle’s theorem, typically studied in first-semester calculus, provides some constraints on the ordering of these roots. However, not all root sequences that are allowed by Rolle’s theorem occur for polynomials with all real roots. We use elementary methods to prove several Rolle’s-type theorems that further constrain the orderings of the roots of polynomials and their derivatives. |
Keywords
Rolle's theorem, polynomial root sequences
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Mathematical Subject Classification
Primary: 26A06
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Milestones
Received: 5 August 2021
Revised: 30 December 2021
Accepted: 31 December 2021
Published: 7 January 2023
Communicated by Michael Dorff
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Authors |
| Laura J. Batts | |
| Department of Mathematics Anderson University Anderson, IN United States |
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| Megan E. Moran | |
| Department of Mathematics Anderson University Anderson, IN United States |
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| Courtney K. Taylor | |
| Department of Mathematics Anderson University Anderson, IN United States |
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