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Black Book Advanced Problems in MathematicsMathematicsApplication of Derivatives

For which of the following function(s) Lagrange's mean value theorem is not applicable in [1, 2] ?

Options

  1. Af(x) = cases 3 2 - x & , x < 3 2 ( 3 2 - x )^2 & , x 3 2 cases
  2. Bf(x) = cases (x - 1) x - 1 & , x 1 1 & , x = 1 cases
  3. Cf(x) = (x - 1)|x - 1|
  4. Df(x) = |x - 1|

Correct answer

A. f(x) = cases 3 2 - x & , x < 3 2 ( 3 2 - x )^2 & , x 3 2 cases

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