Literaturnachweis - Detailanzeige
| Autor/inn/en | Attanucci, Frank J.; Losse, John |
|---|---|
| Titel | Inherited Symmetry |
| Quelle | In: AMATYC Review, 29 (2008) 2, S.9-13 (5 Seiten)
PDF als Volltext |
| Sprache | englisch |
| Dokumenttyp | gedruckt; online; Zeitschriftenaufsatz |
| ISSN | 0740-8404 |
| Schlagwörter | Calculus; Mathematics Instruction; Equations (Mathematics); Mathematical Concepts; Teaching Methods |
| Abstract | In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the point: (a, 0), determines the symmetry of the antiderivative of f defined by F(x) = integral [superscript x] [subscript a] of f(t)dt + F(a). We conclude with an example that shows how our results lead to a "two-line proof" that the graph of any cubic function is symmetric with respect to its point of inflection. (As Provided). |
| Anmerkungen | American Mathematical Association of Two-Year Colleges. 5983 Macon Cove, Memphis, TN 38134. Tel: 901-333-4643; Fax: 901-333-4651; e-mail: amatyc@amatyc.org; Web site: http://www.amatyc.org |
| Erfasst von | ERIC (Education Resources Information Center), Washington, DC |
| Update | 2017/4/10 |
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