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: 60

Answer

\[y = 2ex - e\]

Work Step by Step

\[\begin{gathered} y = x{e^x} \hfill \\ Evaluate\,\,the\,\,function\,\,at\,\,x = 1 \hfill \\ y\,\left( 1 \right) = \,\left( 1 \right){e^{\,\left( 1 \right)}} \hfill \\ y\,\left( 1 \right) = e \hfill \\ P\,oint\,\,\,\left( {1,e} \right) \hfill \\ Find\,\,the\,\,deriva\,tive\,\,of\,\,the\,\,function \hfill \\ {y^,} = \,\,{\left[ {x{e^x}} \right]^,} \hfill \\ Use\,\,the\,\,product\,\,rule \hfill \\ {y^,} = x{e^x} + {e^x} \hfill \\ Evaluate\,\,{y^,}\,\,at\,\,x = 1 \hfill \\ m = {y^,}\,\left( 1 \right) = e + e \hfill \\ m = 2e \hfill \\ Use\,\,the\,\,point\, - slope\,\,form \hfill \\ y - {y_1} = m\,\left( {x - {x_1}} \right) \hfill \\ y - e = 2e\,\left( {x - 1} \right) \hfill \\ y - e = 2ex - 2e \hfill \\ y = 2ex - e \hfill \\ \end{gathered} \]
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