Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.7 - Derivatives and Rates of Change - 2.7 Exercises - Page 151: 53


a. The meaning $f'(x)$ is the rate of change of the production cost; dollars/ounce. b. Increases to $17$ dollars/ounce. c. Short term: decrease; long term: increase

Work Step by Step

a. The meaning $f'(x)$ is the rate of change of the production cost with respect to the number of ounces of gold. The unit is dollars/ounce. b. The value of $f'(800) = 17$ means that after $800$ ounces of produced gold, then the rate/cost of production increases to $17$ dollars/ounce. c. The short term $f'(x)$ could decrease due to the amount of gold deposits the mine has. However, in the long term it would cost more to extract the gold deposits, so the $f'(x)$ will increase.
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