Calculus: Early Transcendentals 8th Edition

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

Chapter 10 - Review - True-False Quiz - Page 689: 9



Work Step by Step

By rotating and translating the parabola, we can assume that it has an equation of the form as $y=cx^{2}$ where $c>0$. The tangent at the point $(a,ca^{2})$ is the line $y-ca^{2}=2ca(x-a)y$ $=2cax-ca^{2}$ The tangent meets the parabola at the points $(x,cx^{2})$ where $cx^{2}=2cax-ca^{2}$ Thus, $x^{2}=2ax-a^{2}$ $x^{2}-2ax+a^{2}=0$ $(x-a)^{2}=0$ This implies $x=a$ Therefore, the tangent meets the parabola at the point $(a,ca^{2})$ at exactly one point. Hence, the given statement is true.
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.