# Misc 13 - Chapter 6 Class 12 Application of Derivatives

Last updated at Jan. 7, 2020 by Teachoo

Last updated at Jan. 7, 2020 by Teachoo

Transcript

Misc 13 Find the points at which the function f given by f (๐ฅ) = (๐ฅโ2)^4 (๐ฅ+1)^3 has (i) local maxima (ii) local minima (iii) point of inflexion f(๐ฅ)= (๐ฅโ2)^4 (๐ฅ+1)3 Finding fโ(๐) fโ(๐ฅ) = (๐ ((๐ฅ โ 2)^4 (๐ฅ + 1)^3 ))/๐๐ฅ = ใ((๐ฅโ2)^4 )^โฒ (๐ฅ+1)ใ^3+((๐ฅ+1)^3 )^โฒ (๐ฅโ2)^4 Using product rule as (๐ข๐ฃ)^โฒ=๐ข^โฒ ๐ฃ+๐ฃ^โฒ ๐ข = 4(๐ฅโ2)^3 (๐ฅ+1)^3+3(๐ฅ+1)^2 (๐ฅโ2)^4 = (๐ฅโ2)^3 (๐ฅ+1)^2 [4(๐ฅ+1)+3(๐ฅโ2)] = (๐ฅโ2)^3 (๐ฅ+1)^2 [4๐ฅ+4+3๐ฅโ6] = (๐ฅโ2)^3 (๐ฅ+1)^2 [7๐ฅโ2] Putting fโ(๐)=๐ (๐ฅโ2)^3 (๐ฅ+1)^2 (7๐ฅโ2)=0 Hence, ๐ฅ=2 & ๐ฅ=โ1 & ๐ฅ=2/7 = 0.28 (๐ฅโ2)^3 = 0 ๐ฅ โ 2 = 0 ๐ฅ=2 (๐ฅ+1)^2=0 (๐ฅ+1)=0 ๐ฅ = โ1 7๐ฅ โ 2 = 0 7๐ฅ = 2 ๐ฅ = 2/7 Thus ๐ฅ=โ1 is a point of inflexion ๐ฅ=2/7 is point of maxima & ๐ฅ=2 is point of minima

Miscellaneous

Misc 1
Important

Misc 2 Important

Misc 3 Important

Misc 4

Misc 5 Important

Misc 6 Important

Misc 7

Misc 8 Important

Misc 9 Important

Misc 10

Misc 11 Important

Misc 12 Important

Misc 13 Important You are here

Misc 14 Important

Misc 15 Important

Misc 16 Important

Misc 17 Important

Misc 18 Important

Misc. 19

Misc 20 Important

Misc 21 Important

Misc 22

Misc. 23 Important

Misc 24 Important

Chapter 6 Class 12 Application of Derivatives

Serial order wise

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.