Calculus 10th Edition

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

Chapter 2 - Differentiation - Review Exercises: 3

Answer

$f'(x) = 2x - 4$

Work Step by Step

$f(x) = x^{2} -4x + 5$ $f'(x) = \lim\limits_{h \to 0} \frac{(x+h)^{2} - 4(x+h) + 5 - (x^{2} - 4x+5)}{h}$ $f'(x) = \lim\limits_{h \to 0} \frac{x^{2} + 2xh + h^{2} -4x-4h + 5 - x^{2} +4x-5}{h}$ $f'(x) = \lim\limits_{h \to 0} \frac{2xh + h^{2} -4h}{h}$ $f'(x) = \lim\limits_{h \to 0} \frac{h(2x + h -4)}{h}$ $f'(x) = \lim\limits_{h \to 0} (2x + h -4)$ $f'(x) = \lim\limits_{h \to 0} (2x + (0) -4)$ $f'(x) = 2x - 4$
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