# Ex 6.1, 1 - Chapter 6 Class 12 Application of Derivatives

Last updated at July 18, 2019 by Teachoo

Last updated at July 18, 2019 by Teachoo

Transcript

Ex 6.1,1 Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm (b) r = 4 cm Radius of circle = ๐ & let A be the area of circle We need to find rate of change of Area w. r. t Radius i.e. we need to calculate ๐๐ด๏ทฎ๐๐๏ทฏ We know that Area of Circle = ๐๐๏ทฎ2๏ทฏ ๐๐ด๏ทฎ๐๐๏ทฏ = ๐ ๐๐๏ทฎ2๏ทฏ๏ทฏ๏ทฎ๐๐๏ทฏ ๐๐ด๏ทฎ๐๐๏ทฏ = ๐ ๐ (๐๏ทฎ2๏ทฏ)๏ทฎ๐๐๏ทฏ๏ทฏ ๐๐ด๏ทฎ๐๐๏ทฏ = ๐ 2๐๏ทฏ ๐๐ด๏ทฎ๐๐๏ทฏ = 2๐ ๐ โข when r = 3 cm ๐๐ด๏ทฎ๐๐๏ทฏ = 2rฯ Putting r = 3 cm ๐๐ด๏ทฎ๐๐๏ทฏ๏ทฏ๏ทฎ๐ = 3๏ทฏ= 2(3) ฯ ๐๐ด๏ทฎ๐๐๏ทฏ๏ทฏ๏ทฎ๐ = 3๏ทฏ = 6 ฯ Since Area is in cm2 & radius is in cm ๐๐ด๏ทฎ๐๐๏ทฏ = 6ฯ ๐๐๐๏ทฎ๐๐๏ทฏ Hence Area is increasing at the rate of 6ฯ cm2/ cm when r = 3 cm (ii) r = 4 cm ๐๐ด๏ทฎ๐๐๏ทฏ = 2rฯ Putting r = 4 cm ๐๐ด๏ทฎ๐๐๏ทฏ = 2(4)ฯ ๐๐ด๏ทฎ๐๐๏ทฏ = 8 ฯ Since Area is in cm2 & radius is in cm ๐ ๐จ๏ทฎ๐ ๐๏ทฏ = 8ฯ ๐๐๐๏ทฎ๐๐๏ทฏ Hence Area is increasing at the rate of 8ฯ cm2/cm when r = 4 cm

Finding rate of change

Example 1

Ex 6.1, 1 You are here

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.