# Example 2 - Chapter 6 Class 12 Application of Derivatives

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 2 The volume of a cube is increasing at a rate of 9 cubic centimeters per second. How fast is the surface area increasing when the length of an edge is 10 centimeters ? Let 𝑥 be length of side V be volume t be time per second Now , we know that Volume of cube = (side)3 V = 𝑥3 Also it is given that Volume of cube is increasing at rate of 9 cubic cm/sec. Therefore 𝑑𝑉𝑑𝑡 = 9 Putting V = 𝑥3 𝑑𝑥3𝑑𝑡 = 9 𝑑𝑥3𝑑𝑡 . 𝑑𝑥𝑑𝑥 = 9 𝑑𝑥3𝑑𝑥 . 𝑑𝑥𝑑𝑡 = 9 3𝑥2 . 𝑑𝑥𝑑𝑡 = 9 𝑑𝑥𝑑𝑡 = 93𝑥2 𝑑𝑥𝑑𝑡 = 3𝑥2 Also, We know that Surface area = 6 side2 S = 6𝑥2 Now, we need to find Increase in surface Area as compared to time i.e. 𝑑𝑆𝑑𝑡 𝑑𝑆𝑑𝑡 = 𝑑(6𝑥2)𝑑𝑡 = 𝑑6𝑥2𝑑𝑡 . 𝑑𝑥𝑑𝑥 = 6 . 𝑑(𝑥2)𝑑𝑥 . 𝑑𝑥𝑑𝑡 = 6 . (2x) . 𝑑𝑥𝑑𝑡 = 12𝑥 . 𝒅𝒙𝒅𝒕 = 12𝑥 . 𝟑𝒙𝟐 = 36𝑥 Thus, 𝑑𝑠𝑑𝑡 = 36𝑥 When 𝑥= 10 cm 𝑑𝑠𝑑𝑡 = 3610 𝑑𝑠𝑑𝑡 = 3.6 Since surface area is in cm2 & time is in seconds, 𝑑𝑠𝑑𝑡 = 3.6 𝑐𝑚2𝑠 𝒅𝒔𝒅𝒕 = 3.6 cm2 /s

Finding rate of change

Example 1

Ex 6.1, 1

Ex 6.1,17

Example 5

Ex 6.1,15 Important

Example 6

Ex 6.1,16

Ex 6.1,18

Example 2 You are here

Ex 6.1,2

Example 49

Example 3

Ex 6.1,5 Important

Ex 6.1,3

Ex 6.1,6

Ex 6.1,12

Ex 6.1,13 Important

Misc. 19

Ex 6.1,14

Example 43 Important

Ex 6.1,4 Important

Example 42 Important

Example 4 Important

Ex 6.1,7

Ex 6.1,8

Ex 6.1,9

Ex 6.1,11 Important

Misc 3 Important

Ex 6.1,10 Important

Example 44 Important

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.