1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
  3. Ex 6.2
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Ex 6.2, 6 (e) - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by Teachoo

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

    3. Ex 6.2

    Ex 6.3 →
Ex 6.3 →
Chapter 6 Class 12 Application of Derivatives
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo