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

Example 6 - Chapter 6 Class 12 Application of Derivatives - Part 2
Example 6 - Chapter 6 Class 12 Application of Derivatives - Part 3

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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 = 𝒅𝑹/𝒅𝒙 Given, Total revenue = R (π‘₯) = 3π‘₯2 + 36π‘₯ + 5 We need to find marginal revenue when π‘₯ = 5 i.e. MR when π‘₯ = 5 MR = 𝑑(𝑅(π‘₯))/𝑑π‘₯ MR = (𝑑 (3π‘₯2 + 36π‘₯ + 5) )/𝑑π‘₯ MR = (𝑑(3π‘₯2))/𝑑π‘₯ + (𝑑(36π‘₯))/𝑑π‘₯ + (𝑑(5))/𝑑π‘₯ MR = 3 (𝑑(π‘₯2))/𝑑π‘₯ + 36 (𝑑(π‘₯))/𝑑π‘₯ + 0 MR = 3 Γ— 2π‘₯ + 36 MR = 6π‘₯ + 36 MR when π‘₯ = 5 MR = 6 (5) + 36 MR = 30 + 36 MR = 66 Hence, the required marginal revenue is Rs. 66

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.