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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

Harvey Mudd College

University of Nottingham

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

03:48

Investigate the family of …

01:12

05:43

Describe how the graph of …

07:24

09:49

13:14

03:45

00:57

03:06

04:26

No transcript available

Numerade Educator

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