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

Transcript

Ex 6.1,18 The total revenue in Rupees received from the sale of 𝑥 units of a product is given by R(𝑥) = 3𝑥2 + 36𝑥 + 5. The marginal revenue, when 𝑥 = 15 is (A) 116 (B) 96 (C) 90 (D) 126 Since Marginal Revenue is Rate of change in Total Revenue w.r.t no of unit sold Let MR = Marginal cost R(𝑥)= Total Revenue 𝑥= no. of unit sold So, MR = 𝑑(𝑅(𝑥))/𝑑𝑥 …(1) It is Given that R(𝑥)=3𝑥^2+36𝑥+15 We need to find marginal Revenue when 𝑥 = 15 i.e. MR at 𝑥 = 15 MR = 𝑑(𝑅(𝑥))/𝑑𝑥 MR = 𝑑(3𝑥^2 + 36𝑥 + 5)/𝑑𝑥 MR = 𝑑(3𝑥^2 )/𝑑𝑥+𝑑(36𝑥)/𝑑𝑥+𝑑(5)/𝑑𝑥 MR = 3 𝑑(𝑥^2 )/𝑑𝑥+36 𝑑(𝑥)/𝑑𝑥+0 MR = 3 × 2𝑥+36 MR = 6𝑥+36 MR when 𝒙 = 15 MR = 6(15)+36 MR = 90 + 36 MR = 126 Hence Marginal Revenue is Rs. 126 Thus, D is the correct Answer