Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 3 - The Derivative - Chapter Review - Review Exercises - Page 188: 12



Work Step by Step

A function must be continuous at a point for the derivative to exist there. But just because a function is continuous at a point does not mean the derivative necessarily exists. The derivative exists when a function $f$ satisfies all of the following conditions at a point: 1. $f$ is continuous, 2. $f$ is smooth 3. $f$ does not have a vertical tangent line.
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