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: 60

Answer

\[ = 4x + 2h - 3\]

Work Step by Step

\[\begin{gathered} f\,\left( x \right) = 2{x^2} - 3x + 1 \hfill \\ \hfill \\ Use{\text{ }}the{\text{ }}definition{\text{ }}of{\text{ }}derivative \hfill \\ \hfill \\ \frac{{f\,\left( {x + h} \right) - f\,\left( x \right)}}{h} = \frac{{2\,{{\left( {x + h} \right)}^2} - 3\,\left( {x + h} \right) + 1 - 2{x^2} + 3x - 1}}{h} \hfill \\ \hfill \\ multiply \hfill \\ \hfill \\ = \frac{{2{x^2} + 4xh + 2{h^2} - 3x - 3h + 1 - 2{x^2} + 3x - 1}}{h} \hfill \\ \hfill \\ simplify \hfill \\ \hfill \\ = \frac{{4xh + 2{h^2} - 3h}}{h} \hfill \\ \hfill \\ = \frac{{h\,\left( {4x + 2h - 3} \right)}}{h} \hfill \\ \hfill \\ = 4x + 2h - 3 \hfill \\ \end{gathered} \]
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