Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.1 Definition of the Derivative - Exercises - Page 103: 25


$$ f(-2+h)=\frac{1}{-2+h}$$ $$\frac{f(a+h)-f(a)}{h}= -\frac{1}{3}$$

Work Step by Step

Since $ f(x)=\frac{1}{x}$, then $ f(-2+h)=\frac{1}{-2+h}$. The quotient difference is given by $$\frac{f(a+h)-f(a)}{h}=\frac{f(-1.5)-f(-2)}{0.5}=\frac{-\frac{1}{1.5}+\frac{1}{2}}{0.5}=-\frac{1}{3}$$
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