Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 13 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - Section 13.4 The Tangent Problem; The Derivative - 13.4 Assess Your Understanding - Page 917: 21

Answer

$-4$

Work Step by Step

Consider that the tangent line contains the point $(x, c)$. The slope of the tangent line to the graph of $f(x)$ at $(x, c)$ can be written as $f'(x) =\lim\limits_{x \to c} \dfrac{f(x)-f(c)}{x-c}$ Consider $c=3$ and $f(x)=-4x+5$. Thus, we have: $f'(x) =\lim\limits_{x \to 3} \dfrac{f(x)-f(3)}{x-3} \\=\lim\limits_{x \to 3} \dfrac{-4x+5-(-7)}{x-3} \\=\lim\limits_{x \to 3} \dfrac{-4(x-3)}{x-3}\\=-4 $
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