# Example 6 - Chapter 6 Class 12 Application of Derivatives

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 6 The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 3x2 + 36x + 5. Find the marginal revenue, when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant. Marginal revenue is rate of change of total revenue w. r. t the number of unit sold Let MR be marginal revenue Given, R is total revenue. & ๐ฅ is number of units sold. So, MR = ๏ท๐๐ ๏ทฎ๐๐ฅ๏ทฏ Given, Total revenue = R (๐ฅ) = 3๐ฅ2 + 36๐ฅ + 5 We need to find marginal revenue when ๐ฅ = 5 i.e. MR when ๐ฅ = 5 MR = ๏ท๐๏ท๐ ๏ท๐ฅ๏ทฏ๏ทฏ๏ทฎ๐๐ฅ๏ทฏ MR = ๏ท๐ ๏ท3๐ฅ2 + 36๐ฅ + 5๏ทฏ ๏ทฎ๐๐ฅ๏ทฏ MR = ๏ท๐(3๐ฅ2)๏ทฎ๐๐ฅ๏ทฏ + ๏ท๐(36๐ฅ)๏ทฎ๐๐ฅ๏ทฏ + ๏ท๐(5)๏ทฎ๐๐ฅ๏ทฏ MR = 3 ๏ท๐(๐ฅ2)๏ทฎ๐๐ฅ๏ทฏ + 36 ๏ท๐(๐ฅ)๏ทฎ๐๐ฅ๏ทฏ + 0 MR = 3 ร 2๐ฅ + 36 MR = 6๐ฅ + 36 MR when ๐ฅ = 5 MR = 6 (5) + 36 MR = 30 + 36 MR = 66 Hence, the required marginal revenue is Rs. 66

Examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6 You are here

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

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.