**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.

Descriptors: Calculus, Mathematics Instruction, Equations (Mathematics), Mathematical Concepts, Teaching Methods

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