Ex 6.2

Chapter 6 Class 12 Application of Derivatives
Serial order wise

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### Transcript

Ex 6.2, 6 Find the intervals in which the following functions are strictly increasing or decreasing: (e) (đĽ + 1)^3 (đĽ â 3)^3 f(đĽ) = (đĽ+1)3 (đĽâ3)3 Calculating fâ(đ) f(đĽ) = (đĽ+1)3 (đĽâ3)3 fâ(đĽ)= ă[(đĽ+1)^3]ă^â˛ (đĽâ3)^3 +[(đĽâ3)3]^â˛ (đĽ+1)^3 fâ(đĽ)=3(đĽ+1)2(đĽâ3)3 + 3(đĽâ3)2(đĽ+1)3 fâ(đĽ)=3(đĽ+1)2(đĽâ3)2 ((đĽâ3)+ (đĽ+1)) fâ(đĽ)=3(đĽ+1)2(đĽâ3)2 (2đĽâ2) fâ(đ)= 6(đ+đ)đ (đâđ)đ (đâđ) Putting fâ(đ)=đ 6(đĽ+1)2 (đĽâ3)2 (đĽâ1) = 0 Hence, đĽ = â1 , 3 & 1 Plotting values of x on real line. Note that: fâ(đĽ) = 6 (đ+đ)^đ (đâđ)^đ (đĽâ1) Hence, f is strictly increasing for 1 < đĽ < 3 & đĽ > 3 i.e. (1, 3) and (3, â) f is strictly decreasing for đĽ < â1 & â1<đĽ< 1 i.e. (ââ, â1) and (â 1, 1)