Calculus: Early Transcendentals 8th Edition

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

Chapter 3 - Review - Exercises - Page 269: 92

Answer

(a) $C'(x) = 2-0.04~x+0.00021~x^2$ (b) $C'(100) = 0.1$ When the production level is 100 units, the additional cost of producing each item is $\$0.10$ (c) The cost of producing the 101st item is $\$0.10$ The value of $C'(100)$ is a very good approximation of the cost of producing the 101st item.

Work Step by Step

(a) $C(x) = 920+2x-0.02~x^2+0.00007~x^3$ We can find the marginal cost function: $C'(x) = 2-0.04~x+0.00021~x^2$ (b) We can find $C'(100)$: $C'(100) = 2-0.04~(100)+0.00021~(100)^2$ $C'(100) = 2-4+2.1$ $C'(100) = 0.1$ When the production level is 100 units, the additional cost of producing each item is $\$0.10$ (c) We can find the total cost of producing 101 items: $C(101) = 920+2(101)-0.02~(101)^2+0.00007~(101)^3$ $C(101) = \$990.10$ We can find the total cost of producing 100 items: $C(100) = 920+2(100)-0.02~(100)^2+0.00007~(100)^3$ $C(100) = \$990.00$ We can find the cost of producing the 101st item: $C(101)- C(100) = \$990.10 - \$990 = \$0.10$ The cost of producing the 101st item is $\$0.10$ The value of $C'(100)$ is a very good approximation of the cost of producing the 101st item.
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