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NDA2017MathematicsContinuity and DifferentiabilityActual

A function is defined as follows: f( x )= array cc - x x ^2 , & x 0 0, & x =0 array . Which one of the following is correct in respect of the above function?

Options

  1. Af( x ) is continuous at x =0 but not differentiable at x =0
  2. Bf(x) is continuous as well as differentiable at x =0
  3. Cf( x ) is discontinuous at x =0
  4. DNone of the above

Correct answer

C. f( x ) is discontinuous at x =0

Step-by-step solution

f(x)= array l -x x^2 , x 0 0, x=0 array .= array l -x |x| , x 0 0, x=0 . array . f (0+ h )= - h ~h =-1 ; f (0- h )= h ~h =1 So, f ( x ) is discontinuous at x =0 .

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