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Ex 6.3
Last updated at April 16, 2024 by Teachoo
Ex 6.3, 29 The maximum value of ă[đĽ(đĽâ1)+1]ă^(1/3) 0 ⤠x ⤠1 is (A) (1/3)^(1/3) (B) 1/2 (C) 1 (D) 0 đ^Ⲡ(đĽ)=1/3 (đĽ^2âđĽ+1)^((â2)/3) (2đĽâ1) đ^Ⲡ(đĽ)=1/(3(đĽ^2 â đĽ + 1)^(2/3) ) .(2đĽâ1) đ^Ⲡ(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 đĽ=1/2 Since, 0 ⤠x ⤠1 Hence, critical points are đĽ=0 ,1/2 , & 1 Hence, Maximum value is 1 at đĽ=0 , 1 â´ Hence, correct answer is C