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: 22



Work Step by Step

We do what we have to according to the exercise: $$f'(1)=\lim_{x\to 1}\frac{f(x)-f(1)}{x-1}=\lim_{x\to 1}\frac{-4+3x-(-1)}{x-1}=\lim_{x\to 1}\frac{-3+3x}{x-1}=\lim_{x\to 1}\frac{3(x-1)}{x-1}=\lim_{x\to 1}3=3.$$
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