Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Review - Concept Check: 16

Answer

1) The function can have a discontinuity (blue line); 2) The function can have a cusp (red line).

Work Step by Step

1) The function can be discontinuous for some $a$. Since all differentiable functions are continuous, if the function has a discontinuity, then it is not differentiable (blue line). 2) The function can have a cusp at some $a$. In that case at $x=a$ the function has two different tangents with different slopes and because the derivative is unique, at the cusp the function is not differentiable (red line).
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