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: 14

Answer

$7$

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: $f'(x)=\lim\limits_{h \to 0}\frac{(7(x+h)-3)-(7x-3)}{h}$ $f'(x)=\lim\limits_{h \to 0}\frac{7x+7h-3-7x+3}{h}$ $f'(x)=\lim\limits_{h \to 0}\frac{7h}{h}$ $f'(x)=7$ (the $x$- and $h$-values will cancel each other out in many situations)
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