Ex 6.2,6 - Chapter 6 Class 12 Application of Derivatives - Part 11

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Ex 6.2,6 - Chapter 6 Class 12 Application of Derivatives - Part 12

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Ex 6.2,6 - Chapter 6 Class 12 Application of Derivatives - Part 13 Ex 6.2,6 - Chapter 6 Class 12 Application of Derivatives - Part 14

  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

Transcript

Ex 6.2, 6 Find the intervals in which the following functions are strictly increasing or decreasing: (e) (๐‘ฅ + 1)^3 (๐‘ฅ โ€“ 3)^3 f(๐‘ฅ) = (๐‘ฅ+1)3 (๐‘ฅโˆ’3)3 Calculating fโ€™(๐’™) f(๐‘ฅ) = (๐‘ฅ+1)3 (๐‘ฅโˆ’3)3 fโ€™(๐‘ฅ)= ใ€–[(๐‘ฅ+1)^3]ใ€—^โ€ฒ (๐‘ฅโˆ’3)^3 +[(๐‘ฅโˆ’3)3]^โ€ฒ (๐‘ฅ+1)^3 fโ€™(๐‘ฅ)=3(๐‘ฅ+1)2(๐‘ฅโˆ’3)3 + 3(๐‘ฅโˆ’3)2(๐‘ฅ+1)3 fโ€™(๐‘ฅ)=3(๐‘ฅ+1)2(๐‘ฅโˆ’3)2 ((๐‘ฅโˆ’3)+ (๐‘ฅ+1)) fโ€™(๐‘ฅ)=3(๐‘ฅ+1)2(๐‘ฅโˆ’3)2 (2๐‘ฅโˆ’2) fโ€™(๐’™)= 6(๐’™+๐Ÿ)๐Ÿ (๐’™โˆ’๐Ÿ‘)๐Ÿ (๐’™โˆ’๐Ÿ) Putting fโ€™(๐’™)=๐ŸŽ 6(๐‘ฅ+1)2 (๐‘ฅโˆ’3)2 (๐‘ฅโˆ’1) = 0 Hence, ๐‘ฅ = โ€“1 , 3 & 1 Plotting values of x on real line. Note that: fโ€™(๐‘ฅ) = 6 (๐’™+๐Ÿ)^๐Ÿ (๐’™โˆ’๐Ÿ‘)^๐Ÿ (๐‘ฅโˆ’1) Hence, f is strictly increasing for 1 < ๐‘ฅ < 3 & ๐‘ฅ > 3 i.e. (1, 3) and (3, โˆž) f is strictly decreasing for ๐‘ฅ < โ€“1 & โˆ’1<๐‘ฅ< 1 i.e. (โ€“โˆž, โ€“1) and (โ€“ 1, 1)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.