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Describe how the graph of $ f $ varies as $ c $ varies. Graph several members of the family to illustrate the trends that you discover. In particular, you should investigate how maximum and minimum points and inflection points move when $ c $ changes. You should also identify any transitional values of $ c $ at which basic shape of the curve changes.

$ f(x) = \dfrac{cx}{1 + c^2x^2} $

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Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 6

Graphing with Calculus and Calculators

Derivatives

Differentiation

Volume

Missouri State University

Campbell University

Harvey Mudd College

University of Nottingham

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