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: 29


$$\langle 4-4t,16-32t \rangle $$

Work Step by Step

Since $ r (t)=\langle t^2,t^4 \rangle, $ then $ r' (t)=\langle 2 t,4t^3 \rangle $ then, the parametrization of the tangent line at $ t=-2$ is given by $$ L(t)=r (-2)+tr'(-2)\\ =\langle 4,16 \rangle +t \langle-4, -32 \rangle \\ =\langle 4-4t,16-32t \rangle \\ $$
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