Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.1 Exercises: 16

Answer

$f'(x)=-\frac{2}{3}$

Work Step by Step

To take the derivative of a function using the limit process, plug into the equation $f'(x)=\lim\limits_{h \to 0}\frac{f(x+h)-f(x)}{h}$ and simplify: $f'(x)=\lim\limits_{h \to 0}\frac{(5-\frac{2}{3}(x+h))-(5-\frac{2}{3}x)}{h}$ $f'(x)=\lim\limits_{h \to 0}\frac{5-\frac{2}{3}h-\frac{2}{3}x-5+\frac{2}{3}x}{h}$ $f'(x)=\lim\limits_{h \to 0}\frac{-\frac{2}{3}h}{h}$ $f'(x)=-\frac{2}{3}$
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