# Ex 6.2, 6 (e) - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by Teachoo

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

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 April 16, 2024 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)