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NDA2017MathematicsContinuity and DifferentiabilityActual

If f(x)=x( x - x+1 ) , then f(x) is

Options

  1. Acontinuous but not differentiable at x=0
  2. Bdifferentiable at x=0
  3. Cnot continuous at x=0
  4. DNone of the above

Correct answer

B. differentiable at x=0

Step-by-step solution

aligned & f(x)=x( x - x+1 ) & f(x)= x( x - x+1 )( x + x+1 ) ( x x+1 ) aligned = x(x-x-1) x + x+1 = -x x + x+1 Hence, f ( x ) is continuous as well as differentiable at x =0 .

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