Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.1 Definition of the Derivative - Exercises - Page 103: 14


For $7\lt x\lt 9$

Work Step by Step

The slope of the tangent line at any point $ x\gt7$ in the domain of the function is negative. As the derivative at a point is defined as the slope of the tangent line at that point, this implies that $ f'(x)\lt0$ for $ x\gt7$ where $ x $ is in the domain of the function. In other words, $ f'(x)\lt0$ for $7\lt x\lt9 $ (The end-point 9 is excluded as no right-hand derivative exists at x=9).
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