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JEE Main2008MathematicsContinuity and DifferentiabilityActual

Let f(x)= array ll (x-1) ( 1 x-1 ), & if x 1 0, & if x=1 array . . Then which one of the following is true?

Options

  1. Af is neither differentiable at x=0 nor at x=1
  2. Bf is differentiable at x=0 and at x=1
  3. Cf is differentiable at x =0 but not at x =1
  4. Df is differentiable at x =1 but not at x =0

Correct answer

A. f is neither differentiable at x=0 nor at x=1

Step-by-step solution

f^ (1)= _ h 0 f(1+h)-f(1) h aligned & f^ (1)= _ h 0 (1+h-1) ( 1 1+h-1 )-0 h = _ h 0 h h ( 1 h ) & f^ (1)= _ h 0 ( 1 h ) aligned f is not differentiable at x=1 . Similarly, f^ (0)= _ h 0 f(h)-f(0) h f^ (0)= _ h 0 (h-1) ( 1 h-1 )- (1) h f is also not differentiable at x =0 .

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