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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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