Suppose to tal cost indollars from the production of X printers is given by C/X=.000xt o005x²+28X+ 3000 Find the average rate ot change of total changes from 300' to 400 cost 'when production
Suppose to tal cost indollars from the production of X printers is given by C/X=.000xt o005x²+28X+ 3000 Find the average rate ot change of total changes from 300' to 400 cost 'when production
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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![**Title: Understanding Cost Functions and Average Rate of Change**
**Content:**
Suppose the total cost in dollars from the production of \( x \) printers is given by the function:
\[ C(x) = 0.0001x^3 + 0.005x^2 + 28x + 3000 \]
**Objective:**
Find the average rate of change of the total cost when production changes from 300 to 400 units.
**Explanation:**
The average rate of change of a function over an interval \([a, b]\) can be computed using the formula:
\[ \text{Average Rate of Change} = \frac{C(b) - C(a)}{b - a} \]
In this scenario, substitute \( a = 300 \) and \( b = 400 \) into the cost function \( C(x) \) to calculate the total costs at these production levels and find the average rate of change. This calculation will help us understand how the cost increases as the production increases from 300 units to 400 units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a799525-bc02-4aa7-a724-19d6c1834605%2Fff38b368-f378-463d-8013-46a08b26eb6a%2Fz7hpx88_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Cost Functions and Average Rate of Change**
**Content:**
Suppose the total cost in dollars from the production of \( x \) printers is given by the function:
\[ C(x) = 0.0001x^3 + 0.005x^2 + 28x + 3000 \]
**Objective:**
Find the average rate of change of the total cost when production changes from 300 to 400 units.
**Explanation:**
The average rate of change of a function over an interval \([a, b]\) can be computed using the formula:
\[ \text{Average Rate of Change} = \frac{C(b) - C(a)}{b - a} \]
In this scenario, substitute \( a = 300 \) and \( b = 400 \) into the cost function \( C(x) \) to calculate the total costs at these production levels and find the average rate of change. This calculation will help us understand how the cost increases as the production increases from 300 units to 400 units.
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