The maximum value of [x (x - 1) + 1 ] ^{ (1/3) } , 0 ≤ đĽ ≤ 1 is:
(a) 0 (b) 1/2 (c) 1 (d) â(1/3)
This question is inspired from Ex 6.5,29 (MCQ) - Chapter 6 Class 12 - Application of Derivatives
CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
Last updated at April 16, 2024 by Teachoo
This question is inspired from Ex 6.5,29 (MCQ) - Chapter 6 Class 12 - Application of Derivatives
Question 43 The maximum value of ["đĽ (đĽ â 1) + 1" ]^(1/3) , 0 â¤ đĽ â¤ 1 is: (a) 0 (b) 1/2 (c) 1 (d) â(1/3) Let f(đĽ)=[đĽ(đĽâ1)+1]^(1/3) Finding fâ(đ) đ(đĽ)=[đĽ[đĽâ1]+1]^(1/3) đ(đĽ)=[đĽ^2âđĽ+1]^(1/3) đ^â˛ (đĽ)=(đ(đĽ^2 â đĽ + 1)^(1/3))/đđĽ đ^â˛ (đĽ)=1/3 (đĽ^2âđĽ+1)^(1/3 â 1) . đ(đĽ^2 â đĽ + 1)/đđĽ đ^â˛ (đĽ)=1/3 (đĽ^2âđĽ+1)^((â2)/3) (2đĽâ1) đ^â˛ (đĽ)=1/(3(đĽ^2 â đĽ + 1)^(2/3) ) .(2đĽâ1) đ^â˛ (đĽ)=(2đĽ â 1)/(3(đĽ^2 â đĽ + 1)^(2/3) ) Putting fâ(đ)=đ (2đĽâ1)/(3(đĽ^2 â đĽ + 1)^(2/3) )=0 2đĽâ1=0 2đĽ=1 đ=đ/đ Since, 0 â¤ x â¤ 1 Hence, critical points are đ=đ ,đ/đ , & 1 Hence, Maximum value is 1 at đĽ=0 , 1 So, the correct answer is (C)