CBSE Class 12 Sample Paper for 2025 Boards
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CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Oct. 3, 2024 by Teachoo
This question is similar to Chapter 6 Class 12 Application of Derivatives - Ex 6.1
Please check the question here
Question 22 The cost (in rupees) of producing 𝑥 items in factory, each day is given by 𝐶(𝑥)=0.00013𝑥^3+0.002𝑥^2+5𝑥+2200 Find the marginal cost when 150 items are produced.Since Marginal Cost is Rate of change in Total Cost w.r.t No of items produced Let MC be marginal cost So, MC = 𝒅𝑪/𝒅𝒙 Given, Total Cost = C(𝑥) =0.00013𝑥^3+0.002𝑥^2+5𝑥+2200 We need to find MC when 𝑥=150 Putting 𝒙=𝟏𝟓𝟎 MC = 0.00039〖(𝟏𝟓𝟎)〗^𝟐 + 𝟎.𝟎𝟎𝟒 × 𝟏𝟓𝟎+𝟓 MC = 39/100000 × 22500+4/1000 × 150+5 MC = 39/1000 × 225+4/100 × 15+5 MC = 𝟖𝟕𝟕𝟓/𝟏𝟎𝟎𝟎 +𝟔𝟎/𝟏𝟎𝟎 +𝟓 MC = 8.775+0.6+5 MC = 14.375 Hence, the Required Marginal cost is Rs. 14.375
