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MHT CET202124 Sep 2021Evening ShiftMathematicsContinuity and DifferentiabilityActual

If f ( x )= array ll x , & for x 0 0, & for x >0 array . , then the function f ( x ) at x =0 is

Options

  1. Anot continuous and not differentiable
  2. Bnot continuous but differentiable
  3. Ccontinuous but not differentiable
  4. Dcontinuous and differentiable

Correct answer

C. continuous but not differentiable

Step-by-step solution

aligned & f ( x )= x , if x 0 & =0, if x>0 & _ x 0⁻ f(x)= _ n 0 x=0 and _ x 0⁺ f(x)=0 & f (0)=0 & f ^ ( x )=1, if x 0 & =0, if x>0 & aligned Thus f(x) is continuous at x=0 aligned f ^ ( x ) & =1, & & if x 0 & =0, & & if x >0 aligned Thus f ( x ) is not differentiable at x =0 .

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