A truck has a minimum speed of 14 mph in high gear. When traveling x mph, the truck burns diesel fuel at the rate of 1225 gal 0.0043315 + x mile Assuming that the truck can not be driven over 59 mph and that diesel fuel costs $1.96 a gallon, find the following. (a) The steady speed that will minimize the cost of the fuel for a 500 mile trip. x = (b) The steady speed that will minimize the total cost of a 500 mile trip if the driver is paid $13 an hour. (c) The steady speed that will minimize the total cost of a 390 mile trip if the driver is paid $23 an hour. x =
A truck has a minimum speed of 14 mph in high gear. When traveling x mph, the truck burns diesel fuel at the rate of 1225 gal 0.0043315 + x mile Assuming that the truck can not be driven over 59 mph and that diesel fuel costs $1.96 a gallon, find the following. (a) The steady speed that will minimize the cost of the fuel for a 500 mile trip. x = (b) The steady speed that will minimize the total cost of a 500 mile trip if the driver is paid $13 an hour. (c) The steady speed that will minimize the total cost of a 390 mile trip if the driver is paid $23 an hour. x =
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem Details:**
A truck has a minimum speed of 14 mph in high gear. When traveling \( x \) mph, the truck burns diesel fuel at the rate of:
\[
0.0043315 \left( \frac{1225}{x} + x \right) \text{ gal/mile}
\]
Assuming that the truck cannot be driven over 59 mph and that diesel fuel costs $1.96 a gallon, find the following:
**(a)** The steady speed that will minimize the cost of the fuel for a 500 mile trip.
\[ x = \]
**(b)** The steady speed that will minimize the total cost of a 500 mile trip if the driver is paid $13 an hour.
\[ x = \]
**(c)** The steady speed that will minimize the total cost of a 390 mile trip if the driver is paid $23 an hour.
\[ x = \]
**Note:** You can earn partial credit on this problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84577f47-6855-4e4f-91d0-241ebc051b86%2F5084e564-9bd8-46b1-bc7d-5ef6f2d10f27%2Fegl4zdu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Details:**
A truck has a minimum speed of 14 mph in high gear. When traveling \( x \) mph, the truck burns diesel fuel at the rate of:
\[
0.0043315 \left( \frac{1225}{x} + x \right) \text{ gal/mile}
\]
Assuming that the truck cannot be driven over 59 mph and that diesel fuel costs $1.96 a gallon, find the following:
**(a)** The steady speed that will minimize the cost of the fuel for a 500 mile trip.
\[ x = \]
**(b)** The steady speed that will minimize the total cost of a 500 mile trip if the driver is paid $13 an hour.
\[ x = \]
**(c)** The steady speed that will minimize the total cost of a 390 mile trip if the driver is paid $23 an hour.
\[ x = \]
**Note:** You can earn partial credit on this problem.
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