Calculus: Early Transcendentals 8th Edition

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

Chapter 4 - Section 4.9 - Antiderivatives - 4.9 Exercises - Page 356: 47

Answer

$f(x)=-\ln|x|+(\ln 2)x-\ln 2$

Work Step by Step

$f''(x)=x^{-2}$ Using the antiderivatives table, $f'(x)=\displaystyle \frac{x^{-1}}{-1}+C=-\frac{1}{x}+C$ Using the antiderivatives table, $f(x)=-\ln|x|+Cx+D$ $\left\{\begin{array}{llll} f(1)=0 & \Rightarrow & 0+C+D=0 & \\ & & D=-C & \\ & & & \\ f(2)=0 & \Rightarrow & & -\ln 2+2C-C=0\\ & & & C=\ln 2\\ & & & D=-\ln 2 \end{array}\right.$ $f(x)=-\ln|x|+(\ln 2)x-\ln 2$
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