Continuity and DifferentiabilityHard

Question

The set of all points, where the function f(x) is differentiable, is

Options

A.(- ∞, ∞)
B.(0, ∞)
C.(- ∞, 0)(0, ∞)
D.(0, ∞)

Solution

Given, f(x)
∴       f′(x)
⇒       f′(x)
∴       RHD at x = 0 ⇒
        and LHD at x = 0
⇒      
Hence, f(x) is differentiable for all x

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