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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