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 105: 69

Answer

The mean of these two symmetric difference quotients is $-0.39375 \mathrm{kph}\times\mathrm{km} / \mathrm{car}$.

Work Step by Step

Let $S(q)$ be the function determining $S$ given $q$. The symmetric difference quotient with $h=10$ is $$ S^{\prime}(80) \approx \frac{S(90)-S(70)}{20}=\frac{60-67.5}{20}=-0.375 $$ with $h=20$ $$ S^{\prime}(80) \approx \frac{S(100)-S(60)}{40}=\frac{56-72.5}{40}=-0.4125 $$ The mean of these two symmetric difference quotients is $-0.39375 \mathrm{kph}\times\mathrm{km} / \mathrm{car}$.
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