Ex 6.1,16 - Chapter 6 Class 12 Application of Derivatives
Last updated at April 16, 2024 by Teachoo
Finding rate of change
Example 1
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Chapter 6 Class 12 Application of Derivatives
Concept wise
-
Finding rate of change
- To show increasing/decreasing in whole domain
- To show increasing/decreasing in intervals
- Find intervals of increasing/decreasing
- Finding slope of tangent/normal
- Finding point when tangent is parallel/ perpendicular
- Finding equation of tangent/normal when point and curve is given
- Finding equation of tangent/normal when slope and curve are given
- Finding approximate value of numbers
- Finding approximate value of function
- Finding approximate value- Statement questions
- Finding minimum and maximum values from graph
- Local maxima and minima
- Minima/ maxima (statement questions) - Number questions
- Minima/ maxima (statement questions) - Geometry questions
- Absolute minima/maxima
Transcript
Ex 6.1, 16 The total revenue in Rupees received from the sale of 𝑥 units of a product is given by R(𝑥) = 13𝑥2 + 26𝑥 + 15. Find the marginal revenue when 𝑥 = 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(𝑥)=13𝑥^2+26𝑥+15 We need to find marginal revenue when 𝑥 = 7 i.e. MR when 𝒙 = 7 MR = 𝑑(𝑅(𝑥))/𝑑𝑥 MR = ( 𝑑(13𝑥^2 + 26𝑥 + 15))/𝑑𝑥 MR = 𝑑(13𝑥^2 )/𝑑𝑥+𝑑(26𝑥)/𝑑𝑥+𝑑(15)/𝑑𝑥 MR = 13 𝑑(𝑥^2 )/𝑑𝑥+ 26 𝑑(𝑥)/𝑑𝑥+0 MR = 13 × 2𝑥+26 MR = 26𝑥+26 MR = 26 (𝒙+𝟏) We need to find MR when 𝑥=7 Putting 𝑥=7 MR = 26 (7+1) MR = 26 × 8 MR = 208 Hence Required marginal Revenue is Rs 208
