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Finding rate of change

Ex 6.1, 18 - Total revenue is given by R(x) = 3x^2 + 36x + 5. Marginal

Ex 6.1, 18 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.1, 18 - Chapter 6 Class 12 Application of Derivatives - Part 3


Transcript

Ex 6.1, 18 The total revenue in Rupees received from the sale of π‘₯ units of a product is given by R(π‘₯) = 3π‘₯2 + 36π‘₯ + 5. The marginal revenue, when π‘₯ = 15 is (A) 116 (B) 96 (C) 90 (D) 126Marginal 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‘₯ = 15 i.e. MR when π‘₯ = 15 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 = 6𝒙 + 36 MR when 𝒙 = 15 MR = 6(15) + 36 MR = 90 + 36 MR = 126 Hence, the required marginal revenue is Rs. 126 Thus, D is the correct Answer

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.