SI 1ɔnno id C = 5,000x + 125,000 X > 0 where x is the number of machines used in the production process. (a) Find the critical values of this function. (Assume 0 < x < ∞. Enter your answers as a comma X = (b) Over what interval does the average cost decrease? (Enter your answer using interval notatic (c) Over what interval does the average cost increase? (Enter your answer using interval notation Submit Answer
SI 1ɔnno id C = 5,000x + 125,000 X > 0 where x is the number of machines used in the production process. (a) Find the critical values of this function. (Assume 0 < x < ∞. Enter your answers as a comma X = (b) Over what interval does the average cost decrease? (Enter your answer using interval notatic (c) Over what interval does the average cost increase? (Enter your answer using interval notation Submit Answer
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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![The text provided appears to be part of a problem involving calculus and optimization in the context of manufacturing costs. Here's the transcription and explanation:
---
**Problem Description:**
The average cost per unit (denoted as \( \overline{C} \)) in producing a shipment of a certain product is defined by the function:
\[
\overline{C} = \frac{5,000x + 125,000}{x}, \quad x > 0
\]
where \( x \) represents the number of machines used in the production process.
**Tasks:**
(a) **Find the critical values of the function.**
Assume \( 0 < x < \infty \). Enter your answers as a comma-separated list.
\( x = \) [Input Box]
(b) **Determine the interval over which the average cost decreases.**
Enter your answer using interval notation.
[Input Box]
(c) **Determine the interval over which the average cost increases.**
Enter your answer using interval notation.
[Input Box]
**Additional Elements:**
- A "Submit Answer" button is present for input submission.
- This is presented within a digital interface with typical system navigation visible (e.g., search bar, various application icons).
**Instructions for Learners:**
- To solve this problem, you will need to use calculus, specifically finding derivatives to determine critical points and analyze intervals of increase and decrease for the function \( \overline{C}(x) \).
- Consider applying the first derivative test to classify the critical points and establish the behavior of the function on given intervals.
By understanding these principles, you can analyze how changes in the number of machines affect production costs, optimizing for efficiency in a manufacturing setup.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21aa43ce-550d-41c6-9c29-d391c001c38a%2F6a8a0a84-31e0-43d7-8d9c-c802d028a454%2Fmcb7a9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The text provided appears to be part of a problem involving calculus and optimization in the context of manufacturing costs. Here's the transcription and explanation:
---
**Problem Description:**
The average cost per unit (denoted as \( \overline{C} \)) in producing a shipment of a certain product is defined by the function:
\[
\overline{C} = \frac{5,000x + 125,000}{x}, \quad x > 0
\]
where \( x \) represents the number of machines used in the production process.
**Tasks:**
(a) **Find the critical values of the function.**
Assume \( 0 < x < \infty \). Enter your answers as a comma-separated list.
\( x = \) [Input Box]
(b) **Determine the interval over which the average cost decreases.**
Enter your answer using interval notation.
[Input Box]
(c) **Determine the interval over which the average cost increases.**
Enter your answer using interval notation.
[Input Box]
**Additional Elements:**
- A "Submit Answer" button is present for input submission.
- This is presented within a digital interface with typical system navigation visible (e.g., search bar, various application icons).
**Instructions for Learners:**
- To solve this problem, you will need to use calculus, specifically finding derivatives to determine critical points and analyze intervals of increase and decrease for the function \( \overline{C}(x) \).
- Consider applying the first derivative test to classify the critical points and establish the behavior of the function on given intervals.
By understanding these principles, you can analyze how changes in the number of machines affect production costs, optimizing for efficiency in a manufacturing setup.
---
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