Calculus (3rd Edition)

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

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 604: 64


The tangent line is horizontal at the point $(7,-16)$. The tangent line is vertical at the point $(-9,0)$.

Work Step by Step

The slope of the tangent line is given by $dy/dx=y'(t)/x'(t)=(2t-8)/(2t)$. The tangent line is horizontal if $dy/dx=0$. Solving for $t$ we get $t=4$. The corresponding point is $c(4)=(7,-16)$. The tangent line is vertical if $dy/dx$ is infinite. This occurs at $t=0$. The corresponding point is $c(0)=(-9,0)$.
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