Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 1 - Section 1.1 - Functions from the Numerical, Algebraic, and Graphical Viewpoints - Exercises - Page 53: 39


a. $\quad-h(2x+h)$ b. $\quad-2x-h$

Work Step by Step

a. $ f(x+h)=2-(x+h)^{2}=\quad$ ...square of a sum $=2-(x^{2}+2xh+h^{2})$ $=2-x^{2}-2xh-h^{2}$ $f(x+h)-f(x)=2-x^{2}-2xh-h^{2}-(2-x^{2})$ $=2-x^{2}-2xh-h^{2}-2+x^{2}$ $=-2xh-h^{2}$ $=-h(2x+h)$ b. using the result of (a), $\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{-h(2x+h)}{h}=\quad$ .. reduce h, $=-(2x+h)$ $=-2x-h$
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