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: 6

Answer

$f’(2) = 12 $

Work Step by Step

$f(x) = x^3 $ $f’(2) = \lim\limits_{h \to 0} \frac{f(2+h) - f(2) }{h} $ $f’(2) = \lim\limits_{h \to 0} \frac {8 + 12h+6h^2 + h^3 -8}{h} $ $f’(2) = \lim\limits_{h \to 0} (12+6h+12h^2) $ $f’(2) = 12 $
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