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ERIC Number: EJ1175237
Record Type: Journal
Publication Date: 2018
Pages: 3
Abstractor: As Provided
ISSN: ISSN-0020-739X
The Geometric Mean Value Theorem
de Camargo, André Pierro
International Journal of Mathematical Education in Science and Technology, v49 n4 p613-615 2018
In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying Rolle's theorem to a function like h(x) := f(x) - f(a) - f(b) - f(a)/ b - a(x - a). Although short and effective, such reasoning is not intuitive. Perhaps for this reason, Tucker classified the Mean Value Theorem as "a technical existence theorem used to prove intuitively obvious statements". Moreover, he argued that "there is nothing obvious about the Mean Value Theorem without the continuity of the derivative". Under so unfair discrimination, we felt the need to come to the defense of this beautiful theorem in order to clear up these misunderstandings.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A