Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Review - Exercises: 47


$f$ is not differentiable at the points where $x=-4$, $x=-1$, $x=2$ and $x=5$.

Work Step by Step

There are 3 cases at which a function fails to be differentiable at a point: 1) Its graph has a corner or a kink there, since there is no tangent line at a corner or a kink. 2) The graph of the function is not continuous at that point. Not continuous means not differentiable. 3) The graph has a vertical tangent line at that point. Because a vertical tangent line would lead to $\lim\limits_{x\to a}|f'(x)|=\infty$ In this graph, there are 4 points at which function $f$ is not differentiable: 1) The point where $x=-4$, since the graph is not continuous there. 2) The point where $x=-1$, since the graph has a corner / a kink there. 3) The point where $x=2$, since the graph is again not continuous there. 4) The point where $x=5$, since at that point, only a vertical tangent line can be drawn.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.