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BITSAT2017MathematicsContinuity and DifferentiabilityActual

Consider the greatest integer function, defined by f ( x ) = [ x ] , 0 ≤ x < 2 . Then

Options

  1. Af is derivable at x = 1
  2. Bf is not derivable at x = 1
  3. Cf is derivable at x = 2
  4. DNone of these

Correct answer

B. f is not derivable at x = 1

Step-by-step solution

The given function is f x = 0 , 0 ≤ x < 1 1 , 1 ≤ x < 2 Now, LHD = lim x → 1 - f ( x ) - f ( 1 ) x - 1 = lim x → 1 - 0 - 1 x - 1 Which does not exist ∴   f is not derivable at x = 1 .

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