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BITSAT2017MathematicsApplication of DerivativesActual

Rolle's theorem is not applicable for the function f ( x ) = | x | in the interval [ - 1 , 1 ] because

Options

  1. Af ' ( 1 ) does not exist
  2. Bf ' ( - 1 ) does not exist
  3. Cf ( x ) is discontinuous at x = 0
  4. Df ' ( 0 ) does not exist

Correct answer

D. f ' ( 0 ) does not exist

Step-by-step solution

We have, f ( x ) = | x | We know that the function is not differentiable at the sharp edges. Hence, f x is not differentiable at x = 0 . Therefore, Rolle's theorem is not applicable for the function f ( x ) = | x | in [ - 1 , 1 ] ∵   f ' ( 0 ) does not exist.

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