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Finding rate of change

The Total Revenue is given by R(x) = 13x^2 + 26x + 15. Find Marginal

Ex 6.1,16 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.1,16 - Chapter 6 Class 12 Application of Derivatives - Part 3


Transcript

Ex 6.1, 16 The total revenue in Rupees received from the sale of π‘₯ units of a product is given by R(π‘₯) = 13π‘₯2 + 26π‘₯ + 15. Find the marginal revenue when π‘₯ = 7. 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‘₯)=13π‘₯^2+26π‘₯+15 We need to find marginal revenue when π‘₯ = 7 i.e. MR when 𝒙 = 7 MR = 𝑑(𝑅(π‘₯))/𝑑π‘₯ MR = ( 𝑑(13π‘₯^2 + 26π‘₯ + 15))/𝑑π‘₯ MR = 𝑑(13π‘₯^2 )/𝑑π‘₯+𝑑(26π‘₯)/𝑑π‘₯+𝑑(15)/𝑑π‘₯ MR = 13 𝑑(π‘₯^2 )/𝑑π‘₯+ 26 𝑑(π‘₯)/𝑑π‘₯+0 MR = 13 Γ— 2π‘₯+26 MR = 26π‘₯+26 MR = 26 (𝒙+𝟏) We need to find MR when π‘₯=7 Putting π‘₯=7 MR = 26 (7+1) MR = 26 Γ— 8 MR = 208 Hence Required marginal Revenue is Rs 208

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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.