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: 57


a) $ f′(x)=\dfrac{1}{2\sqrt x}$ b) $\dfrac{1}{12}, \dfrac{1}{18}$

Work Step by Step

a) Now, $ f′(x)=\lim_\limits{ h\to 0} \dfrac{f(x+h)-f(x)}{h}$ or, $=\lim_\limits{ h\to 0} \dfrac{\sqrt{x+h}-\sqrt x}{h}$ or, $=\lim_\limits{ h\to 0} \dfrac{1}{\sqrt{x+h}+\sqrt x}$ or, $=\dfrac{1}{\sqrt{x+0}+\sqrt x}$ or, $ f′(x)=\dfrac{1}{2\sqrt x}$ b) $ f′(36)=\dfrac{1}{2 \sqrt{36}}=\dfrac{1}{12}$ and $ f′(81)=\dfrac{1}{2 \sqrt{81}}=\dfrac{1}{18}$
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