Calculus 10th Edition

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

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.1 Exercises - Page 326: 66

Answer

$y=\displaystyle \frac{3}{2}x-\frac{3}{2}$

Work Step by Step

Use: Theorem 5.2 :properties of ln(x), Theorem 5.3.1:$\ \ \ (\displaystyle \ln x)^{\prime}=\frac{1}{x}$ -------------------- $y=f(x)=\ln x^{3/2}$=... property (3) of ln...$=\displaystyle \frac{3}{2}\ln x$ $f^{\prime}(x)=\displaystyle \frac{3}{2}\cdot\frac{1}{x}=\frac{3}{2x}$ The slope of the tangent at (1,0) is $f^{\prime}(1)=\displaystyle \frac{3}{2}$ Point-slope equation of the tangent line: $y-y_{0}=m(x-x_{0})$ $y-0=\displaystyle \frac{3}{2}(x-1)$ $y=\displaystyle \frac{3}{2}x-\frac{3}{2}$ For (b) and (c), see image attached.
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