Ex 6.1,4 - 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
Ex 6.1, 4 An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of cube increasing when the edge is 10 cm long?Let ๐ be the edge of cube. & V be the volume of cube. Given that Edge of cube is increasing at the rate of 3 cm/ sec โด ๐ ๐/๐ ๐ = 3 cm/sec We need to calculate how fast volume of cube increasing when edge is 10 cm i.e. we need to find ๐ ๐ฝ/๐ ๐ when ๐ฅ = 10 cm We know that Volume of cube = (Edge)3 V = ๐ฅ3 Differentiate w.r.t time ๐ ๐ฝ/๐ ๐ = (๐ (๐๐))/๐ ๐ ๐๐/๐๐ก = (๐(๐ฅ3))/๐๐ก ร ๐๐ฅ/๐๐ฅ ๐๐/๐๐ก = (๐(๐ฅ3))/๐๐ฅ ร ๐๐ฅ/๐๐ก ๐๐/๐๐ก = 3๐ฅ2 . ๐ ๐/๐ ๐ ๐๐/๐๐ก = 3๐ฅ2 ร 3 ๐๐/๐๐ก = 9๐ฅ2 When ๐ฅ = 10 โ ๐๐/๐๐กโค|_(๐ฅ =10) = 9(10)2 โ ๐๐/๐๐กโค|_(๐ฅ =10) = 900 Since value is in cm3 & time is in sec ๐ ๐ฝ/๐ ๐ = 900 cm3/sec Hence, volume of a cube is increasing at the rate of 900 cm3/sec
