If is a differentiable function satisfying

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

If ff is a differentiable function satisfying f(1n)=0,∀n≥1,n∈If\left(\frac{1}{n}\right) = 0, \forall n \ge 1, n \in \mathbb{I}, then (1) f(x)=0,x∈(0,1]f(x) = 0, x \in (0, 1] (2) f′(0)=0=f(0)f'(0) = 0 = f(0) (3) f(0)=0f(0) = 0 but f′(0)f'(0) not necessarily zero (4) ∣f(x)∣≤1,x∈(0,1]|f(x)| \le 1, x \in (0, 1]

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