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: 54


$f(x)=x^{3}$ and $a=5$

Work Step by Step

The derivative at a point $a$ is defined as $f'(a)=\lim\limits_{x \to a}\frac{f(x)-f(a)}{x-a}$ But, given that $f'(a)=\lim\limits_{x \to 5}\frac{x^{3}-125}{x-5}\,\,\,\,$ Comparing right-hand sides of both the equations above, we obtain $a=5$ and $f(x)=x^{3}$
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