Ex 6.1,6 - 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
-
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, 6 The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference? Let r be the radius of circle & C be the circumference of circle Given that Radius of a circle is increasing at the rate of 0.7 cm/sec i.e. 𝒅𝒓/𝒅𝒕 = 0.7 cm/sec We need find rate of change of circumference of circle w. r. 𝑡 time i.e. we need to calculate 𝒅𝑪/𝒅𝒕 We know that Circumference of circle = 2πr Now, 𝑑𝐶/𝑑𝑡 = (𝑑(2𝜋𝑟))/𝑑𝑡 𝑑𝐶/𝑑𝑡 = 2π 𝒅𝒓/𝒅𝒕 𝑑𝐶/𝑑𝑡 = 2π × 0.7 𝑑𝐶/𝑑𝑡 = 1.4π (From (1): 𝑑𝑟/𝑑𝑡 = 5 ) Since circumference is in cm & time is in sec 𝑑𝐶/𝑑𝑡 = 1.4π cm/sec Hence, circumference of circle is increasing at the rate of 1.4π cm/sec
