Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.1 Review of Functions - 1.1 Exercises: 64

Answer

\[ = - a - x - 4\]

Work Step by Step

\[\begin{gathered} f\,\left( x \right) = 4 - 4x - {x^2} \hfill \\ \hfill \\ {\text{Derivative formula}} \hfill \\ \hfill \\ \frac{{f\,\left( x \right) - f\,\left( a \right)}}{{x - a}} = \frac{{4 - 4x - {x^2} - 4 + 4a + {a^2}}}{{x - a}} \hfill \\ \hfill \\ factor\,\,and\,\,\,simplify \hfill \\ \hfill \\ = \frac{{{a^2} - {x^2} + 4\,\left( {a - x} \right)}}{{x - a}} \hfill \\ \hfill \\ \frac{{\,\left( {a - x} \right)\,\left( {a + x} \right) + 4\,\left( {a - x} \right)}}{{x - a}} \hfill \\ \hfill \\ = \frac{{\,\left( {a - x} \right)\,\left( {a + x + 4} \right)}}{{x - a}} \hfill \\ \hfill \\ cancel\,\,\,\,x - a \hfill \\ \hfill \\ = - 1\,\left( {a + x + 4} \right) \hfill \\ \hfill \\ multiply \hfill \\ \hfill \\ = - a - x - 4 \hfill \\ \end{gathered} \]
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