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Home » The maximum value of [x(x-1)+1]^1/3, 0≤x≤1 is (A) (1/3)^1/3 (B) 1/2 (C) 1 (C) 1/3
The maximum value of [x(x-1)+1]^1/3, 0≤x≤1 is (A) (1/3)^1/3 (B) 1/2 (C) 1 (C) 1/3
Applications of Derivatives | CBSE | Class 12 | Exercise 6.5 | Maths | NCERT
The maximum value of [x(x-1)+1]^1/3, 0≤x≤1 is (A) (1/3)^1/3 (B) 1/2 (C) 1 (C) 1/3

Let 

= ,      ……….(i)

  

= 

Now 

   = 0

 

    [Turning point] and it belongs to the given enclosed interval  i.e., [0, 1].

At , from eq. (i),

At   from eq. (i),

At ,  from eq. (i),

  Maximum value of  is 1.

Therefore, The correct option is option (C).

i

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