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 - 14.4 The Tangent Problem; The Derivative - 14.4 Assess Your Understanding - Page 898: 29



Work Step by Step

Factor each polynomial: $$f'(1)\\=\lim_{x\to 1}\frac{f(x)-f(1)}{x-1}\\=\lim_{x\to 1}\frac{x^3+x^2-2x-((1)^3+(1)^2-2(1))}{x-1}\\=\lim_{x\to 1}\frac{x^3+x^2-2x}{x-1}\\=\lim_{x\to 1}\frac{(x(x+2)(x-1)}{(x-1)}.$$ Cancel the common factors: $$\lim_{x\to 1}x(x+2)\\=1(1+2)=3$$
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