Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Section 3.3 - Derivatives of Trigonometric Functions - 3.3 Exercises - Page 196: 26

Answer

$y-(\pi+3)=(3-3\sqrt 3)(x-\frac{\pi}{3})$

Work Step by Step

To find the equation of the tangent line, we first need the slope, which we can find by taking the derivative of $y=3x+6cosx$ using the power rule and trig function identities. $$y'=3-6sinx$$ Using the point given, we can easily write the equation of the line in point-slope form $y-y_{1}=m(x-x_1)$ to get: $y-(\pi+3)=(3-3\sqrt 3)(x-\frac{\pi}{3})$
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