Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.2 Working with Derivatives - 3.2 Exercises - Page 143: 29

Answer

$a.$ At $t=0$; $b.$ Positive; $c.$ Decreasing; $d.$ The graph is on the figure below.

Work Step by Step

$a.$ The rate of change of the charge $Q'$ is the greatest at the point where the tangent to the graph of $Q(t)$ has the steepest upward slope which is for $x=0$; $b.$ It is positive because the charge is only increasing. $c.$ $Q'$ is decreasing because we see that as time goes by (as $t$ becomes bigger) the slope of the tangent to the graph is smaller and smaller. $d.$ The general shape of the graph of $Q'$ can be deduced from the shape of the graph of $Q$. We see that it starts from some positive value and keeps decreasing and asymptotically approaches zero because the graph of $Q$ becomes increasingly horizontal as $t$ grows and thus the slope of its tangent tends to zero. The graph is on the figure below.
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.