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 1
Important
Not in Syllabus - CBSE Exams 2021

Misc 2 Important

Misc 3 Important Not in Syllabus - CBSE Exams 2021

Misc 4

Misc 5 Important

Misc 6 Important

Misc 7 You are here

Misc 8 Important

Misc 9 Important

Misc 10

Misc 11 Important

Misc 12 Important

Misc 13 Important

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

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.