Continuity and DifferentiabilityHard
Question
The set of all points, where the function f(x)
is differentiable, is
is differentiable, isOptions
A.(- ∞, ∞)
B.(0, ∞)
C.(- ∞, 0)
(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
∴ 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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