# Example 1 - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 27, 2018 by Teachoo

Last updated at Dec. 27, 2018 by Teachoo

Transcript

Example 1 Find the rate of change of the area of a circle per second with respect to its radius r when r = 5 cm. We have to find rate of change of area of circle with respect to radius i.e. we need to find (๐(๐ด๐๐๐ ๐๐ ๐๐๐๐๐๐))/(๐ (๐๐๐๐๐ข๐ ๐๐ ๐๐๐๐๐๐)) = ๐๐ด/๐๐ We know that Area of circle = ฯ r2 A = ฯr2 Finding ๐๐ด/๐๐ ๐๐ด/๐๐ = (๐(๐๐2))/๐๐ = ฯ ((๐2))/๐๐ = ฯ (2 . r2 โ1) = 2ฯ r For r = 5 cm ๐๐ด/๐๐ = 2ฯ (5) . = 10ฯ cm2/sec

Finding rate of change

Example 1
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Ex 6.1,1

Ex 6.1,17

Example 5

Ex 6.1,15

Example 6

Ex 6.1,16

Ex 6.1,18

Example 42

Example 2

Ex 6.1,2

Example 49

Example 3

Ex 6.1,5

Ex 6.1,3

Ex 6.1,6

Ex 6.1,12

Ex 6.1,13

Misc. 19

Ex 6.1,14

Example 43

Ex 6.1,4

Example 4

Ex 6.1,7

Ex 6.1,8

Ex 6.1,9

Ex 6.1,11

Ex 6.1,10

Misc 3

Example 44

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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.