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Question

The set of all points, where the function f(x)=x1+|x| is differentiable is

A
(,)
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B
[0,)
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C
(,0)(0,)
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D
(0,)
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Solution

The correct option is A (,)
f(x)=x1+|x| is differentiable everywhere except probably at x = 0.
For x = 0,
(LHD at x=0)=limh0 f(0h)f(0)h=limh0 h1+h0h=1(RHD at x=0)=limh0 f(0+h)f(0)h=limh0 h1+h0h=1(LHD at x=0)=(RHD at x=0)
Therefore, f is differentiable at x = 0.
Hence, f is differentiable in (,)

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