If f(x) is continuous and differentiable function and f(1/n…

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

Published by: CGP EDU Academic Team

Published on: August 12, 2026

If f(x) is continuous and differentiable function and f(1/n) = 0 n ≥ 1 and n ∈ ∈ I, then:

f(x) = 0, x ∈ ∈ (0, 1]

f(0) = 0, f’(0) = 0

f(0) = 0 = f’(0), x Ù (0, 1]

f(0) = 0 and f’(0) nedd not to be zero

Text Solution

Verified by Experts

The correct answer is:

Given that f(x) is a continuous and differentiable function and x = n, n ∈ ∈ I

∴ ∴

Since R.H.L. = 0, ∴ ∴ f(0) = 0 for f(x) to be continuous.

Also f’(0) =

[Using f(0) = 0] = 0 [ ∴ ∴ f(0 + ) = 0]

Hence f(0) = 0, f’(0) = 0.

Previous Question Next Question

Get practice questions, solutions, and test series in one place.

Share your experience with this question and solution.

Send your comment, doubt, correction, or feedback to admin.

What students say about this solution

No reviews yet. Be the first to write a review.