Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 14 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - Chapter Review - Review Exercises - Page 907: 34



Work Step by Step

Factor each polynomial: $$f'(0)\\=\lim_{x\to 0}\frac{f(x)-f(0)}{x-0}\\=\lim_{x\to 0}\frac{x^2-3x-((0)^2-3(0))}{x}\\=\lim_{x\to 0}\frac{x^2-3x}{x}\\=\lim_{x\to 0}\frac{x(x-3)}{x}.$$ Cancel the common factors: $$\lim_{x\to 0}x-3\\=0-3=-3$$
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