oblem: After being built, a car must be painted. The revenue, R, in dollars when x cars are painted can be modelled by the function R(x) = 1000x – 0.5x². a) Determine the average rate of change of revenue when painting 200 to 300 cars. b) Estimate the instantaneous rate of change of revenue after painting 1600 cars. c) Interpret the results found in parts a) and b).
oblem: After being built, a car must be painted. The revenue, R, in dollars when x cars are painted can be modelled by the function R(x) = 1000x – 0.5x². a) Determine the average rate of change of revenue when painting 200 to 300 cars. b) Estimate the instantaneous rate of change of revenue after painting 1600 cars. c) Interpret the results found in parts a) and b).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem: After being built, a car must be painted. The revenue, R, in dollars when x cars are painted
can be modelled by the function R(x) = 1000x – 0.5x².
a) Determine the average rate of change of revenue when painting 200 to 300 cars.
b) Estimate the instantaneous rate of change of revenue after painting 1600 cars.
c) Interpret the results found in parts a) and b).
Expert Solution
Step 1
In this question, concept of average and instantaneous change is applied.
Using the slope formula from algebra, the average rate of change calculates the slope of the secant line. Using derivatives, the instantaneous rate of change estimates the slope of the tangent line.
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