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Question

If the function f(x) has LHD and RHD at x0, which are finite and equal, then f(x) is differentiable at x0, always.

A

True

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B

False

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Solution

The correct option is A

True


Fit is not sufficient for LHD and RHD to be equal rthe function f(x) must be continuous at x0.

For example, consider the function f(x)=x2x.

LHD at x=0 is 1

RHD at x=0 is 1

But f(x) is not difined at x=0 i.e., f(x) is discontinuous at z=0 it is not differentiable at x=0


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