Ex 6.3,29 (MCQ) - Chapter 6 Class 12 Application of Derivatives

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Ex 6.3, 29 The maximum value of 〖[𝑥(𝑥−1)+1]〗^(1/3) 0 ≤ x ≤ 1 is (A) (1/3)^(1/3) (B) 1/2 (C) 1 (D) 0 𝑓^′ (𝑥)=1/3 (𝑥^2−𝑥+1)^((−2)/3) (2𝑥−1) 𝑓^′ (𝑥)=1/(3(𝑥^2 − 𝑥 + 1)^(2/3) ) .(2𝑥−1) 𝑓^′ (𝑥)=(2𝑥 − 1)/(3(𝑥^2 − 𝑥 + 1)^(2/3) ) Putting f’(𝒙)=𝟎 (2𝑥−1)/(3(𝑥^2 − 𝑥 + 1)^(2/3) )=0 2𝑥−1=0 2𝑥=1 𝑥=1/2 Since, 0 ≤ x ≤ 1 Hence, critical points are 𝑥=0 ,1/2 , & 1 Hence, Maximum value is 1 at 𝑥=0 , 1 ∴ Hence, correct answer is C

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo