The function f(x) = is

Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

Differentiable everywhere

Continuous but not differentiable at x=0

Not a continuous function

None of these

Text Solution

Verified by Experts

The correct answer is:

The range of the function x 3 is (– ∞ ∞ , ∞ ∞ ), and the range of f(x) is [0, ∞ ∞ ), f is clearly differentiable except possibly at the point x = 0.

Now, clearly by definition Rf ′ ′ (0) = L f ′ ′ (0) = 0

so that, f is differentiable at x = 0 and hence every where

Alternative solution:

Here f (x) =

so that f ′ ′ (x) =

⇒ ⇒ the function is differentiable everywhere including x = 0

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