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Question

If f(x)=|logx10| x ϵ(0,) then


A
f(x) is continuous in
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B

f(x) is differentiable in (0, ∞)

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C

f(x) is continuous but not differentiable in (0, ∞)

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D
None of these
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Solution

The correct options are
A f(x) is continuous in
C

f(x) is continuous but not differentiable in (0, ∞)


Clearly, we see f(x) is continuous from (0,) but there is a sharp edge at 1 which means LHD and RHD

are finite but not equal. Therefore f(x) is continuous in (0,) but not differentiable throughout (0,). It

is only differentiable in xϵ(0,1) (1,).


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