Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 13 - Section 13.1 - The Indefinite Integral - Exercises - Page 958: 44

Answer

$f(x)=\ln|x|+1.$

Work Step by Step

The tangent line at $(x, f(x))$ has slope $f'(x)$, which is given: $f'(x)=\displaystyle \frac{1}{x}$ So, $f(x)$ is an antiderivative: $f(x)=\displaystyle \int\frac{1}{x}dx=\ln|x|+C.$ The indefinite integral gives us a collection of functions. To find the exact function, we find C. We are given that $f(1)=1$, so $1=\ln 1+C$ $1=0+C$ $C=1$ So, $f(x)=\ln|x|+1.$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.