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: 37


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

Work Step by Step

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