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

True

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False

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Solution

The correct option is B False
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) = $\frac{x^{2}}{x} .$
LHD at x = 0 is 1
RHD at x = 0 is 1

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

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

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