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: 53

Answer

\[y = - 2x - 4\]

Work Step by Step

\[\begin{gathered} y = {x^2} - 6x\,\,\,,\,\,\,x = 2 \hfill \\ Evaluate\,\,the\,\,function\,\,at\,\,x = 2 \hfill \\ y\,\left( 2 \right) = \,{\left( 2 \right)^2} - 6\,\left( 2 \right) \hfill \\ y\,\left( 2 \right) = - 8 \hfill \\ Point\,\,\,\left( {2, - 8} \right) \hfill \\ Find\,\,the\,\,derivative\,\,of\,\,the\,\,fuction \hfill \\ {y^,} = \,{\left( {{x^2} - 6x} \right)^,} \hfill \\ {y^,} = 2x - 6 \hfill \\ m = {y^,}\,\left( 2 \right) = 2\,\left( 2 \right) - 6 \hfill \\ m = - 2 \hfill \\ Point - slope\,\,form\,\, \hfill \\ y - {y_1} = m\,\left( {x - {x_1}} \right) \hfill \\ y - \,\left( { - 8} \right) = - 2\,\left( {x - 2} \right) \hfill \\ Simplifying \hfill \\ y + 8 = - 2\,\left( {x - 2} \right) \hfill \\ y + 8 = - 2x + 4 \hfill \\ y = - 2x - 4 \hfill \\ \end{gathered} \]
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