Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.3 Exercises: 68

Answer

The equation of the tangent line is $y=2\sqrt{3}x+\dfrac{6-2\sqrt{3}\pi}{3}$.

Work Step by Step

$f'(x)=\dfrac{d}{dx}\sec{x}=\sec{x}\tan{x}$ $f'(\frac{\pi}{3})=(\sec{\frac{\pi}{3}})(tan{\frac{\pi}{3}})=2\sqrt{3}.$ Equation of tangent: $(y-y_0)=m(x-x_0)$ at point $(x_0, y_0)$ and slope $m$. $(y-2)=2\sqrt{3}(x-\frac{\pi}{3}) \rightarrow y=2\sqrt{3}x+\dfrac{6-2\sqrt{3}\pi}{3}$
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