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AP EAMCET2014MathematicsApplication of Derivatives

The value of c in the Lagrange's mean value theorem for f(x)= x-2 in the interval [2,6] is

Options

  1. A9 2
  2. B5 2
  3. C3
  4. D4

Correct answer

C. 3

Step-by-step solution

Given, f(x)= x-2 , x [2,6] We know that, by Lagrange's mean value theorem, their exist c (2,6) such that aligned & f(c)= f(b)-f(a) b-a & = 1 2 c-2 = f(6)-f(2) 6-2 & 1 2 c-2 = 6-2 - 2-2 4 aligned array ll & 1 c-2 = 4 -0 2 & 1 c-2 =1 c-2 =1 & c-2=1 c=3 array

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