Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 14 - Calculus of Vector-Valued Functions - 14.2 Calculus of Vector-Valued Functions - Exercises - Page 720: 13

Answer

$$ r'(t)=\langle 1,2t,3t^2 \rangle,$$ $$ r''(t)=\langle 0,2,6t \rangle .$$

Work Step by Step

Since $ r(t)=\langle t,t^2,t^3 \rangle $, then the derivative $ r'(t)$ is given by $$ r'(t)=\langle 1,2t,3t^2 \rangle,$$ and hence the second derivative $ r''(t)$ is given by $$ r''(t)=\langle 0,2,6t \rangle.$$
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.