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Ex 6.2
Ex 6.2,2
Ex 6.2,3 Important
Ex 6.2,4
Ex 6.2, 5 Important
Ex 6.2, 6 (a)
Ex 6.2, 6 (b) Important
Ex 6.2, 6 (c) Important
Ex 6.2, 6 (d)
Ex 6.2, 6 (e) Important You are here
Ex 6.2, 7
Ex 6.2,8 Important
Ex 6.2,9 Important
Ex 6.2,10
Ex 6.2,11
Ex 6.2, 12 (A)
Ex 6.2, 12 (B) Important
Ex 6.2, 12 (C) Important
Ex 6.2, 12 (D)
Ex 6.2, 13 (MCQ) Important
Ex 6.2,14 Important
Ex 6.2,15
Ex 6.2, 16
Ex 6.2,17 Important
Ex 6.2,18
Ex 6.2,19 (MCQ) Important
Last updated at Aug. 19, 2021 by Teachoo
Ex 6.2, 6 Find the intervals in which the following functions are strictly increasing or decreasing: (e) (đĽ + 1)^3 (đĽ â 3)^3 f(đĽ) = (đĽ+1)3 (đĽâ3)3 Calculating fâ(đ) f(đĽ) = (đĽ+1)3 (đĽâ3)3 fâ(đĽ)= ă[(đĽ+1)^3]ă^Ⲡ(đĽâ3)^3 +[(đĽâ3)3]^Ⲡ(đĽ+1)^3 fâ(đĽ)=3(đĽ+1)2(đĽâ3)3 + 3(đĽâ3)2(đĽ+1)3 fâ(đĽ)=3(đĽ+1)2(đĽâ3)2 ((đĽâ3)+ (đĽ+1)) fâ(đĽ)=3(đĽ+1)2(đĽâ3)2 (2đĽâ2) fâ(đ)= 6(đ+đ)đ (đâđ)đ (đâđ) Putting fâ(đ)=đ 6(đĽ+1)2 (đĽâ3)2 (đĽâ1) = 0 Hence, đĽ = â1 , 3 & 1 Plotting values of x on real line. Note that: fâ(đĽ) = 6 (đ+đ)^đ (đâđ)^đ (đĽâ1) Hence, f is strictly increasing for 1 < đĽ < 3 & đĽ > 3 i.e. (1, 3) and (3, â) f is strictly decreasing for đĽ < â1 & â1<đĽ< 1 i.e. (ââ, â1) and (â 1, 1)