Calculus (3rd Edition)

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

Chapter 3 - Differentiation - Chapter Review Exercises - Page 162: 14


$f'(-1)$, where $f(x)= x^{3}$

Work Step by Step

The derivative of $f(x)$ at a point $a$ is defined as $f'(a)=\lim\limits_{x \to a}\frac{f(x)-f(a)}{x-a}$ Comparing $\lim\limits_{x\to -1}\frac{x^{3}+1}{x+1}$ with the above definition, we get $a=-1$ $f(x)-f(a)=x^{3}+1$ $f(x)=x^{3}$ and $f(a)= f(-1)= (-1)^{3}=-1$ Therefore, the given limit can be expressed as the derivative of $f(x)= x^{3}$ at $x=-1$
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