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KCET2019MathematicsContinuity and Differentiability

Rolle's theorem is not applicable in which one of the following cases?

Options

  1. A( f(x)=x²-x ) in ( [0,1] )
  2. B( f(x)=[x] ) in ( [2.5,2.7] )
  3. C( f(x)=x²-4 x+5 ) in ( [1,3] )
  4. D( f(x)=|x| ) in ( [-2,2] )

Correct answer

D. ( f(x)=|x| ) in ( [-2,2] )

Step-by-step solution

(f(x)=x²-4 x+5 ) (x [1,3] ) ( aligned f(1) &=1-4+5 &=2 f(3) &=9-12+5 &=2 f^ (x) &=2 x-4 _ h 0 f^ (x) &= _ h 0 (2 x-4) &=-4 aligned ) ( ) IInd condition of rolls theorem is not satisfied. ( ) Role theorem not applicable

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