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COMEDK2015MathematicsApplication of Derivatives

The value of c in Lagrange's mean value theorem for the function f(x)= ( x) in the interval [ 6 , 5 6 ] is

Options

  1. A4
  2. B2
  3. C2 3
  4. DNone of these

Correct answer

B. 2

Step-by-step solution

f(x)= ( (x)) is continuous in [ 6 , 5 6 ] and differentiable in ( 6 , 5 6 ) as its derivative f^ (x)= 1 x x= x Now , f ( 6 )= ( ( 6 ) )= ( 1 2 ) ( 5 6 )= ( 5 6 )= ( 6 )= ( 1 2 ) Now, according to Lagrange's mean value theorem, there exists a point c ( 6 , 5 6 ) such that f^ (c)= f ( 6 )-f ( 5 6 ) ( 6 - 5 6 ) c=0 c= 2

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