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The minimum value of the function f(x)= ₀^x d + _x^ / 2 d where x (0, 2 ) , is

Options

  1. A2 ( 2 +1)
  2. B(2 2 +2)
  3. C(2+ 3 )
  4. D(3+ 2 )

Correct answer

A. 2 ( 2 +1)

Step-by-step solution

aligned & f^ (x)= x- cosec x & f^ (x)=0 at x= 4 aligned Also f " ( 4 ) 0 so f(x) is minimum at x= 4 f ( 4 )= ₀^ / 4 d + _ / 4 ^ / 2 cosec d = ( 2 +1 2 -1 )=2 ( 2 +1)

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