Increasing function theorem an alternative for the mean value theorem
Date of Publication
1998
Document Type
Bachelor's Thesis
Degree Name
Bachelor of Science in Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Abstract/Summary
This thesis is based on the article Rethinking Rigor in Calculus: The Role of the Mean Value Theorem by Thomas W. Tucker. It gives a detailed proof of the Increasing Function Theorem independent of the Mean Value Theorem. The Increasing Function Theorem states that if f1(x) >0 on an interval, then f is increasing on that interval. The Immediate Consequences of the Mean Value Theorem were redone using the Increasing Function Theorem so as to illustrate the usefulness of the Increasing Function Theorem. The derivation of Taylor Error Bounds was provided as one of the consequences of the Increasing Function Theorem. Here, the proofs are presented as simply as possible so that they will be understood by students of elementary calculus courses.
Abstract Format
html
Language
English
Format
Accession Number
TU08766
Shelf Location
Archives, The Learning Commons, 12F, Henry Sy Sr. Hall
Physical Description
40 leaves
Keywords
Functions; Mean value theorems (Calculus); Geometry, Infinitesimal
Recommended Citation
Aguilar, R. A., & Alamon, M. D. (1998). Increasing function theorem an alternative for the mean value theorem. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/16495
