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Investigate the family of curves given by $ f(x) = xe^{-cx} $, where $ c $ is a real number. Start by computing the limits as $ x \to \pm \infty $. Identify any transitional values of $ c $ where the basic shape changes. What happens to the maximum or minimum points and inflection points as $ c $ changes? Illustrate by graphing several members of the family.

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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

Campbell University

Oregon State University

Harvey Mudd College

University of Nottingham

Lectures

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Investigate the family of …

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