## Calculus with Applications (10th Edition)

Published by Pearson

# Chapter 4 - Calculating the Derivative - Chapter Review - Review Exercises - Page 245: 54

#### Answer

$y = - 2x + 9$

#### Work Step by Step

$\begin{gathered} y = 8 - {x^2}\,\,,\,\,x = 1 \hfill \\ Evaluate\,\,the\,\,function\,\,at\,\,x = 1 \hfill \\ y\,\left( 1 \right) = 8 - \,{\left( 1 \right)^2} \hfill \\ y\,\left( 1 \right) = 7 \hfill \\ Point\,\,\,\left( {1,7} \right) \hfill \\ Find\,\,the\,\,derivative\,\,of\,\,the\,\,fuction \hfill \\ {y^,} = \,{\left( {8 - {x^2}} \right)^,} \hfill \\ {y^,} = - 2x \hfill \\ m = {y^,}\,\left( 1 \right) = - 2\,\left( 1 \right) \hfill \\ m = - 2 \hfill \\ Point - slope\,\,form\,\, \hfill \\ y - 7 = - 2\,\left( {x - 1} \right) \hfill \\ Simplifying \hfill \\ y - 7 = - 2x + 2 \hfill \\ y = - 2x + 9 \hfill \\ \end{gathered}$

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