Example 6 - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Finding rate of change
Example 1
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Chapter 6 Class 12 Application of Derivatives
Concept wise
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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
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 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 So, MR = 𝒅𝑹/𝒅𝒙 Given, Total revenue = R (𝑥) = 3𝑥2 + 36𝑥 + 5 We need to find marginal revenue when 𝑥 = 5 i.e. MR when 𝑥 = 5 MR = 𝑑(𝑅(𝑥))/𝑑𝑥 MR = (𝑑 (3𝑥2 + 36𝑥 + 5) )/𝑑𝑥 MR = (𝑑(3𝑥2))/𝑑𝑥 + (𝑑(36𝑥))/𝑑𝑥 + (𝑑(5))/𝑑𝑥 MR = 3 (𝑑(𝑥2))/𝑑𝑥 + 36 (𝑑(𝑥))/𝑑𝑥 + 0 MR = 3 × 2𝑥 + 36 MR = 6𝑥 + 36 MR when 𝑥 = 5 MR = 6 (5) + 36 MR = 30 + 36 MR = 66 Hence, the required marginal revenue is Rs. 66
