Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.4 Rates of Change - Exercises - Page 129: 4


$f'(1) = -1$ $f'(2) = -\frac{1}{4}$ $f'(3) = -\frac{1}{9}$

Work Step by Step

Let $f(x) = \frac{1}{x}$ To find the rate of change, we need to find the derivative of the function, which we can do using the power rule: $f(x) = x^{-1}$ $f'(x) = -x^{-2}$ Now, to find the rate at each point, we substitute x for each point given: $f'(1) = -(1)^{-2} = -1$ $f'(2) = -(2)^{-2} = -\frac{1}{4}$ $f'(3) = -(3)^{-2} = -\frac{1}{9}$
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