# Example 5

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 5 The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005 x3 – 0.02 x2 + 30x + 5000 Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output. Marginal cost is the rate of change of total cost w.r.t output (unit produce) Let MC be marginal cost ∴ MC = 𝑑𝐶𝑑𝑥 It is given C(𝑥) = 0.005𝑥3 – 0.02𝑥2 + 30𝑥 + 5000 We need to find marginal cost when 3 unit produced i.e. need to find MC = 𝑑𝐶𝑑𝑥 at 𝑥 = 3 Now, MC = 𝑑(𝑐)𝑑𝑥 MC = 𝑑0.05𝑥3 − 0.02𝑥2 + 30 + 5000𝑑𝑥 MC = 𝑑0.05𝑥3𝑑𝑥 – 𝑑(0.02𝑥2)𝑑𝑥 + 𝑑 (30𝑥)𝑑𝑥 + 𝑑 5000𝑑𝑥 MC = 3 × 0.05x2 – 2 × 0.02x + 30 + 0 MC = 0.015x2 – 0.04x + 30 We need MC at 𝑥 = 3 Putting 𝑥= 3 MC = 0.015(32) – 0.04 (3) + 30 MC = 30.015 Hence, Required marginal cost is Rs. 30.02 (nearly)

Example 1

Example 2

Example 3

Example 4

Example 5 You are here

Example 6

Example 7

Example 8

Example 9

Example 10

Example 11

Example 12

Example 13

Example 14

Example 15

Example 16

Example 17

Example 18

Example 19

Example 20

Example 21

Example 22

Example 23

Example 24

Example 25

Example 26

Example 27

Example 28

Example 29

Example 30

Example 31

Example 32

Example 33

Example 34

Example 35 Important

Example 36

Example 37 Important

Example 38 Important

Example 39

Example 40 Important

Example 41

Example 42

Example 43

Example 44

Example 45

Example 46 Important

Example 47 Important

Example 48

Example 49

Example 50

Example 51

Chapter 6 Class 12 Application of Derivatives

Serial order wise

About the Author

CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .