Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - Review - Exercises - Page 197: 47

Answer

$y= 2\sqrt 3 (x) - (\pi/\sqrt 3) +1 $

Work Step by Step

$ y= 4(sin^{2} x)$ $y' = 8 sinx cosx$ $At (\pi/6, 1)$ $y' = 8 sin (\pi/6) cos (\pi/6)$ $y' = 2\sqrt 3$ Slope is equal to $2\sqrt 3$ Substitue $(\pi/6, 1)$ $1 = 2\sqrt 3 (\pi/6) + b$ $b= 1-2\sqrt 3 (\pi/6)$ $b= 1- (\pi/\sqrt 3)$ Thus the equation is $y= 2\sqrt 3 (x) - (\pi/\sqrt 3) +1 $
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