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Question

If f(x)=|logx10| x ϵ(0,) then


A
f(x) is continuous in (0,)
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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 option is 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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