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Q.

The set of points where the function f(x)=[x]+|1x|,1x3

where [.]  denotes the greatest integer function, is not differentiable, is 

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a

{0,1,2,3,}

b

{-1,0,2}

c

{-1,0,1,2}

d

{1,0,1,2,3}

answer is C.

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Detailed Solution

We have

f(x)=x,    1x<01x,    0x<1x,    1x<21+x,    2x<35,    x=3

Clearly, f (x) is discontinuous at x = 0,1, 2, and 3.

So, it is not differentiable at these points.

At x=-1, we have

limx1+f(x)=limx1+x=1=f(1)

So, it is continuous at x=-1.

Also, (RHD at x=-1)=-1 (a finite number). 

Therefore, f (x) is differentiable at x=-1.

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