If ƒ is an even function such that has some finite non-ze…

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

Published by: CGP EDU Academic Team

Published on: August 11, 2026

If ƒ is an even function such that has some finite non-zero value, then -

ƒ is continuous and derivable at x = 0

ƒ is continuous but not derivable at x = 0

ƒ may be discontinuous at x = 0

None of these

Text Solution

Verified by Experts

The correct answer is:

Let ƒ ′ (0 + ) = = k (say)

∴ ƒ ′ (0 – ) =

= = – k.

 ƒ ′ (0 + ) ≠ ƒ ′ (0 – ), but both are finite,

so ƒ(x) is continuous at x = 0 but not differentiable at x = 0.

Hence is the correct answer.

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