Example 6 - Chapter 6 Class 12 Application of Derivatives
Last updated at May 29, 2018 by Teachoo
Transcript
Example 6 The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 3x2 + 36x + 5. Find the marginal revenue, when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant. Marginal revenue is rate of change of total revenue w. r. t the number of unit sold Let MR be marginal revenue Given, R is total revenue. & ๐ฅ is number of units sold. So, MR = ๏ท๐๐ ๏ทฎ๐๐ฅ๏ทฏ Given, Total revenue = R (๐ฅ) = 3๐ฅ2 + 36๐ฅ + 5 We need to find marginal revenue when ๐ฅ = 5 i.e. MR when ๐ฅ = 5 MR = ๏ท๐๏ท๐ ๏ท๐ฅ๏ทฏ๏ทฏ๏ทฎ๐๐ฅ๏ทฏ MR = ๏ท๐ ๏ท3๐ฅ2 + 36๐ฅ + 5๏ทฏ ๏ทฎ๐๐ฅ๏ทฏ MR = ๏ท๐(3๐ฅ2)๏ทฎ๐๐ฅ๏ทฏ + ๏ท๐(36๐ฅ)๏ทฎ๐๐ฅ๏ทฏ + ๏ท๐(5)๏ทฎ๐๐ฅ๏ทฏ MR = 3 ๏ท๐(๐ฅ2)๏ทฎ๐๐ฅ๏ทฏ + 36 ๏ท๐(๐ฅ)๏ทฎ๐๐ฅ๏ทฏ + 0 MR = 3 ร 2๐ฅ + 36 MR = 6๐ฅ + 36 MR when ๐ฅ = 5 MR = 6 (5) + 36 MR = 30 + 36 MR = 66 Hence, the required marginal revenue is Rs. 66
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Chapter 6 Class 12 Application of Derivatives
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.