Example 6 - Total revenue received from sale of x units - Examples

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Example 6 - Chapter 6 Class 12 Application of Derivatives - Part 2

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Example 6 - Chapter 6 Class 12 Application of Derivatives - Part 3

  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

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 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 So, MR = ๐’…๐‘น/๐’…๐’™ Given, Total revenue = R (๐‘ฅ) = 3๐‘ฅ2 + 36๐‘ฅ + 5 We need to find marginal revenue when ๐‘ฅ = 5 i.e. MR when ๐‘ฅ = 5 MR = ๐‘‘(๐‘…(๐‘ฅ))/๐‘‘๐‘ฅ MR = (๐‘‘ (3๐‘ฅ2 + 36๐‘ฅ + 5) )/๐‘‘๐‘ฅ MR = (๐‘‘(3๐‘ฅ2))/๐‘‘๐‘ฅ + (๐‘‘(36๐‘ฅ))/๐‘‘๐‘ฅ + (๐‘‘(5))/๐‘‘๐‘ฅ MR = 3 (๐‘‘(๐‘ฅ2))/๐‘‘๐‘ฅ + 36 (๐‘‘(๐‘ฅ))/๐‘‘๐‘ฅ + 0 MR = 3 ร— 2๐‘ฅ + 36 MR = 6๐‘ฅ + 36 MR when ๐‘ฅ = 5 MR = 6 (5) + 36 MR = 30 + 36 MR = 66 Hence, the required marginal revenue is Rs. 66

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.