Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

Last updated at Feb. 20, 2021 by Teachoo

Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

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. & 𝑥 is number of units sold. So, MR = 𝑑𝑅𝑑𝑥 Given, Total revenue = R (𝑥) = 3𝑥2 + 36𝑥 + 5 We need to find marginal revenue when 𝑥 = 5 i.e. MR when 𝑥 = 5 MR = 𝑑𝑅𝑥𝑑𝑥 MR = 𝑑 3𝑥2 + 36𝑥 + 5 𝑑𝑥 MR = 𝑑(3𝑥2)𝑑𝑥 + 𝑑(36𝑥)𝑑𝑥 + 𝑑(5)𝑑𝑥 MR = 3 𝑑(𝑥2)𝑑𝑥 + 36 𝑑(𝑥)𝑑𝑥 + 0 MR = 3 × 2𝑥 + 36 MR = 6𝑥 + 36 MR when 𝑥 = 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 9 years. He provides courses for Maths and Science at Teachoo.