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 104: 56


$ f(x)=x^{-1}$ and $ a=\frac{1}{4}$

Work Step by Step

The derivative $ f'(a)$ is defined as $ f'(a)=\lim\limits_{x \to a}\frac{f(x)-f(a)}{x-a}$ Comparing $\lim\limits_{x \to \frac{1}{4}}\frac{x^{-1}-4}{x-\frac{1}{4}}$ with the above definition, we get $ a=\frac{1}{4}$ and $ f(x)=x^{-1}$
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