Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12



Last updated at Jan. 7, 2020 by Teachoo
Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12
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 2 Important
Misc 3 Important Not in Syllabus - CBSE Exams 2021
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 Not in Syllabus - CBSE Exams 2021
Misc 20 Important
Misc 21 Important
Misc 22
Misc. 23 Important
Misc 24 Important
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