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Ex 6.2

Ex 6.2, 1

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

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Ex 6.2,15

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Ex 6.2,17 Important

Ex 6.2,18

Ex 6.2,19 (MCQ) Important

Last updated at May 29, 2023 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^â˛ (đĽâ3)^3 +[(đĽâ3)3]^â˛ (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)