Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 4 - Calculating the Derivative - Chapter Review - Review Exercises: 61

Answer

\[y = x - 1\]

Work Step by Step

\[\begin{gathered} y = \ln x \hfill \\ Evaluate\,\,the\,\,function\,\,at\,\,x = 1 \hfill \\ y = \ln \,\left( 1 \right) = 0 \hfill \\ Point\,\,\,\left( {1,0} \right) \hfill \\ Find\,\,the\,\,deriva\,tive\,\,of\,\,the\,\,function \hfill \\ {y^,} = \,\,{\left[ {\ln x} \right]^,} = \frac{1}{x} \hfill \\ Evaluate\,\,{y^,}\,\left( 1 \right) \hfill \\ m = {y^,}\,\left( 1 \right) = \frac{1}{1} = 1 \hfill \\ m = 1 \hfill \\ Use\,\,the\,\,point\, - slope\,\,form \hfill \\ y - {y_1} = m\,\left( {x - {x_1}} \right) \hfill \\ y - 0 = 1\,\left( {x - 1} \right) \hfill \\ y = x - 1 \hfill \\ \end{gathered} \]
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