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1. Let C(x) = ax² + 2bxr + = for positive constants a, b, c, be the cost of producing z items. (i) Determine the marginal cost dC and the average cost T(x) = C(x) dr (ii) Determine the rate of change of average cost dr For what values of r is < 0 for r in terms of a,b,c. dr average cost decreasing? That is solve (iii) Determine the values of r for which average cost is greater than marginal cost. That is solve C(x) > dC for r in terms of a, b, c. dr

1. Let C(x) = ax² + 2bxr + = for positive constants a, b, c, be the cost of producing z items. (i) Determine the marginal cost dC and the average cost T(x) = C(x) dr (ii) Determine the rate of change of average cost dr For what values of r is < 0 for r in terms of a,b,c. dr average cost decreasing? That is solve (iii) Determine the values of r for which average cost is greater than marginal cost. That is solve C(x) > dC for r in terms of a, b, c. dr

Calculus: Early Transcendentals
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 4 Let \( C(x) = ax^2 + 2bx + \frac{c^2}{a} \) for positive constants \( a, b, c \), be the cost of producing \( x \) items. 1. **Determine the Marginal Cost:** Find \(\frac{dC}{dx}\). 2. **Determine the Average Cost:** Find \(\overline{C}(x) = \frac{C(x)}{x}\). 3. **Rate of Change of Average Cost:** Determine the rate of change \(\frac{d\overline{C}}{dx}\). For what values of \( x \) is the average cost decreasing? Solve \(\frac{d\overline{C}}{dx} < 0\) for \( x \) in terms of \( a, b, c \). 4. **Comparison of Average and Marginal Cost:** Determine the values of \( x \) for which average cost is greater than marginal cost. Solve \(\overline{C}(x) > \frac{dC}{dx}\) for \( x \) in terms of \( a, b, c \). 5. **Expression for Complex Derivative:** What is the expression for \(\frac{d^2}{dx^2}\left(\frac{C(x)}{x}\right) = \frac{d^2 \overline{C}}{dx^2}\)?
Transcribed Image Text:### Problem 4 Let \( C(x) = ax^2 + 2bx + \frac{c^2}{a} \) for positive constants \( a, b, c \), be the cost of producing \( x \) items. 1. **Determine the Marginal Cost:** Find \(\frac{dC}{dx}\). 2. **Determine the Average Cost:** Find \(\overline{C}(x) = \frac{C(x)}{x}\). 3. **Rate of Change of Average Cost:** Determine the rate of change \(\frac{d\overline{C}}{dx}\). For what values of \( x \) is the average cost decreasing? Solve \(\frac{d\overline{C}}{dx} < 0\) for \( x \) in terms of \( a, b, c \). 4. **Comparison of Average and Marginal Cost:** Determine the values of \( x \) for which average cost is greater than marginal cost. Solve \(\overline{C}(x) > \frac{dC}{dx}\) for \( x \) in terms of \( a, b, c \). 5. **Expression for Complex Derivative:** What is the expression for \(\frac{d^2}{dx^2}\left(\frac{C(x)}{x}\right) = \frac{d^2 \overline{C}}{dx^2}\)?
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