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BITSAT 2017
Exam
BITSAT
Year
2017
Subject
Mathematics
Chapter
Application of Derivatives

BITSAT 2017 · Mathematics · Application of Derivatives

Rolle's theorem is not applicable for the function f ( x ) = | x |...

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

Options

  1. Af′(1)f^{'} ( 1 )& does not exist
  2. Bf′(−1)f^{'} ( - 1 ) does not exist
  3. Cf(x)f ( x ) is discontinuous at x=0x = 0
  4. Df′(0)f^{'} ( 0 ) does not exist

Correct answer

D. f′(0)f^{'} ( 0 ) does not exist

Step-by-step solution

We have,

f(x)=∣x∣f ( x ) = | x |

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

We know that the function is not differentiable at the sharp edges. Hence, ff\left(x\right)is not differentiable at&x = 0. Therefore,& Rolle's theorem is not applicable for the function</p><p>f ( x ) = | x |inin[ - 1, 1 ]</p><p></p><p>∵ f^{'} ( 0 ) does not exist.

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