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Ch. 3 - Derivatives
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Briggs 3rd EditionCh. 3 - Derivatives문제 107a
3장, 문제 107a

Suppose the cost of producing x lawn mowers is C(x) = −0.02x²+400x+5000. 
a. Determine the average and marginal costs for x = 3000 lawn mowers.

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To find the average cost, use the formula for average cost: \( \text{Average Cost} = \frac{C(x)}{x} \). Substitute \( C(x) = -0.02x^2 + 400x + 5000 \) and \( x = 3000 \) into the formula.
Calculate \( C(3000) \) by substituting \( x = 3000 \) into the cost function \( C(x) = -0.02x^2 + 400x + 5000 \).
Once you have \( C(3000) \), divide it by 3000 to find the average cost for producing 3000 lawn mowers.
To find the marginal cost, first determine the derivative of the cost function \( C(x) \). The derivative \( C'(x) \) represents the marginal cost.
Calculate \( C'(3000) \) by substituting \( x = 3000 \) into the derivative \( C'(x) \) to find the marginal cost for producing the 3000th lawn mower.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Cost Function

A cost function, such as C(x) = -0.02x² + 400x + 5000, represents the total cost of producing x units of a good. It typically includes fixed costs and variable costs, where the quadratic term indicates how costs change with production levels. Understanding the structure of the cost function is essential for calculating average and marginal costs.
추천 영상:
가이드 코스
06:21
Properties of Functions

Average Cost

The average cost is calculated by dividing the total cost C(x) by the number of units produced, x. It provides insight into the cost per unit at a specific production level. For example, the average cost for producing 3000 lawn mowers can be found by evaluating C(3000) and dividing by 3000, which helps in assessing efficiency and pricing strategies.
추천 영상:
가이드 코스
06:37
Average Value of a Function

Marginal Cost

Marginal cost refers to the additional cost incurred from producing one more unit of a good. It is derived from the derivative of the cost function, C'(x), evaluated at a specific production level. For x = 3000, calculating the marginal cost involves finding C'(3000), which indicates how production decisions impact overall costs and profitability.
추천 영상:
07:32
Example 3: Maximizing Profit
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