Question

If f is a differentiable function satisfying f(1/n) = 0 for all n ≥ 1, n ∈ I, then

(a) f(x) = 0, x ∈ (0, 1]

(b) f'(0) = 0 = f(0)

(c) f(0) = 0 but f'(0) not necessarily zero

(d) | f(x) | ≤ 1, x ∈ (0, 1]

Answer 1

Correct option (b) f'(0) = 0 = f(0)

Explanation :

Since, there are infinitely many points in neighbourhood of x = 0.