Mean, Meaner, and the Meanest Mean Value Theorem

The Mean Value Theorem of the elementary calculus keeps attracting the attention of mathematicians who ponder how to make its proof simple and elegant, how to generalize it, how to use it in proofs of other theorems, and, perversely, how to avoid it. Here, Koliha proves three versions of the Mean Va...

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Bibliographic Details
Published in:The American mathematical monthly 2009-04, Vol.116 (4), p.356-361
Main Author: Koliha, J. J.
Format: Article
Language:English
Subjects:
Calculus
Mathematical functions
Mathematical inequalities
Mathematical intervals
Mathematical theorems
Mathematics education
Mean value theorems
Null set
Open intervals
Proof theory
Theorems
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Summary:The Mean Value Theorem of the elementary calculus keeps attracting the attention of mathematicians who ponder how to make its proof simple and elegant, how to generalize it, how to use it in proofs of other theorems, and, perversely, how to avoid it. Here, Koliha proves three versions of the Mean Value Theorem for complex-valued functions in the form of an inequality, and demonstrates their usefulness in applications. All three versions will be proved using so-called full covers of (a, b).
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2009.11920948