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 7 Find the intervals in which the function f given by f (x) = x3 + 1/๐ฅ^3 , ๐ฅ โ 0 is (i) increasing (ii) decreasing. f(๐ฅ) = ๐ฅ3 + 1/๐ฅ3 Finding fโ(๐) fโ(๐ฅ) = ๐/๐๐ฅ (๐ฅ^3+๐ฅ^(โ3) )^. = 3๐ฅ2 + (โ3)^(โ3 โ 1) = 3๐ฅ2 โ 3๐ฅ^(โ4) = 3๐ฅ^2โ3/๐ฅ^4 = 3(๐ฅ^2โ1/๐ฅ^4 ) f(๐ฅ) = ๐ฅ3 + 1/๐ฅ3 Finding fโ(๐) fโ(๐ฅ) = ๐/๐๐ฅ (๐ฅ^3+๐ฅ^(โ3) )^. = 3๐ฅ2 + (โ3)^(โ3 โ 1) = 3๐ฅ2 โ 3๐ฅ^(โ4) = 3๐ฅ^2โ3/๐ฅ^4 = 3(๐ฅ^2โ1/๐ฅ^4 ) ๐ฅ^3โ1 = 0 ๐ฅ^3= โ1 ๐ฅ = 1 ๐ฅ^3+1 = 0 ๐ฅ3 = โ1 ๐ฅ = โ1 Putting fโ(๐) = 0 3(๐ฅ^2โ1/๐ฅ^4 ) = 0 ๐ฅ^2โ1/๐ฅ^4 = 0 (๐ฅ^6 โ 1)/๐ฅ^4 = 0 ๐ฅ^6โ1 = 0 (๐ฅ^3 )^2โ(1)^2=0 (๐ฅ^3โ1)(๐ฅ^3+1)=0 Hence, ๐ฅ = 1 & โ1 Plotting value of ๐ on real line Thus, ๐ฅ = โ1 & 1 divide the real line into three disjoint intervals i.e. (โโ,โ1)(โ1, 1)& (1,โ) Hence, f(๐ฅ) is strictly increasing on (โโ , โ๐) & (๐ , โ) & strictly decreasing on (โ๐ , ๐)
Miscellaneous
Misc 2 Important
Misc 3 Important Not in Syllabus - CBSE Exams 2021
Misc 4
Misc 5 Important
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Misc 7 You are here
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Misc. 19 Not in Syllabus - CBSE Exams 2021
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