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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 options are
A (,)
B [0, )
C (, 0)(0, )
D (0, )
f(x)=x1+|x|=(x1+x, if x0x1x, if x<0Looking at f(x), we can say that f(x) is differentiable at every where except 0,where we need to check its differentiability.(LHD at x=0)=limh0 f(0h)f(0)h=limh0 h1+h0h= limh011 + h=1(RHD at x=0)=limh0+ f(0+h)f(0)h=limh0+ h1+h0h=limh0+11 + h=1(LHD at x=0)=(RHD at x=0)f is differentiable at x=0.Hence, f is differentiable in (,)

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