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Using high school algebra for a natural approach to derivatives and continuity

Published online by Cambridge University Press:  17 October 2018

R. Michael Range
R. Michael Range*
Affiliation:
Department of Mathematics, State University of New York at Albany, Albany, NY 12222USA e-mail: range@math.albany.edu
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Extract

The quadratic equation is a central topic in high school algebra. It provides the simplest generalisation of the familiar linear equation, and finding its roots introduces students to a non-trivial problem that requires the application of new techniques, such as completing the square and/or factorisation into linear factors involving the roots. It also introduces the student to the phenomenon of repeated roots, which opens the door to a discussion of multiplicities of roots. Furthermore, it naturally exposes the student to the case where the equation has no real roots, a phenomenon that could also be used to introduce the student to complex numbers.

Type
Articles
Information
The Mathematical Gazette , Volume 102 , Issue 555 , November 2018 , pp. 435 - 446
Copyright
Copyright © Mathematical Association 2018 

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References

1. Katz, Victor J., A history of mathematics (3rd edn.), Addison Wesley, Boston (2009).Google Scholar
2. Eves, Howard, An introduction to the history of mathematics (3rd edn.), Holt, Rinehart and Winston, New York (1969).Google Scholar
3. Michael Range, R., Where are limits needed in calculus?, Amer. Math. Monthly 118 (2011) pp. 404–417.Google Scholar
4. Michael Range, R., What is calculus? From simple algebra to deep analysis, World Scientific Publishing, Singapore, London and New York (2015).Google Scholar