Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.7 - Derivatives and Rates of Change - 2.7 Exercises: 39

Answer

$f(x)=x^6$ and $a=2$

Work Step by Step

*Another way to write the derivative of a function $f$ at a number $a$ is $$f'(a)=\lim\limits_{x\to a}\frac{f(x)-f(a)}{x-a}\hspace{0.5cm}(1)$$ Here we have $$f'(a)=\lim\limits_{x\to 2}\frac{x^6-64}{x-2}$$ $$f'(a)=\lim\limits_{x\to 2}\frac{x^6-2^6}{x-2}$$ Now we match the formula found above with the formula of the derivative according to (1). We find that $a=2$, $f(a)=f(2)=2^6$ and $f(x)=x^6$
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