Last updated at April 15, 2021 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 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 ๐น/๐ ๐ Given, Total revenue = R (๐ฅ) = 3๐ฅ2 + 36๐ฅ + 5 We need to find marginal revenue when ๐ฅ = 5 i.e. MR when ๐ฅ = 5 MR = ๐(๐ (๐ฅ))/๐๐ฅ MR = (๐ (3๐ฅ2 + 36๐ฅ + 5) )/๐๐ฅ MR = (๐(3๐ฅ2))/๐๐ฅ + (๐(36๐ฅ))/๐๐ฅ + (๐(5))/๐๐ฅ MR = 3 (๐(๐ฅ2))/๐๐ฅ + 36 (๐(๐ฅ))/๐๐ฅ + 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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About the Author

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.