Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Review Exercises - Page 1179: 55


a) $ f′(x)=6x^2-1$ b) $5,5$

Work Step by Step

a) Now, $ f′(x)=\lim_\limits{ h\to 0} \dfrac{f(x+h)-f(x)}{h}$ or, $=\lim_\limits{ h\to 0} \dfrac{[2(x+h)^3-(x+h)]-(2x^3-x)}{h}$ or, $=\lim_\limits{ h\to 0} \dfrac{6x^2h+6xh^2+2h^3-h}{h}$ or, $=6x^2+6x(0)+2(0)^2-1$ or, $ f′(x)=6x^2-1$ b) $ f′(-1)=6 (-1)^2-1=5$ and $ f′(1)=6 (1)^2-1=5$
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