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ERIC Number: EJ875532
Record Type: Journal
Publication Date: 2008
Pages: 5
Abstractor: As Provided
Reference Count: 0
ISBN: N/A
ISSN: ISSN-0740-8404
Inherited Symmetry
Attanucci, Frank J.; Losse, John
AMATYC Review, v29 n2 p9-13 Spr 2008
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.
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
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A