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AIEEE 2005

JEE Main 2005 Mathematics question on Limits Continuity and Differentiability

If ff is a differentiable function satisfying f(1n)=0,∀ n≥1,n∈If\left(\frac{1}{n}\right) = 0, \forall\ n \geq 1, n \in I, then
  1. A.
    f(x)=0,x∈[0,1]f(x) = 0, x \in [0, 1]
  2. B.
    f′(0)=0=f(0)f'(0) = 0 = f(0)
  3. C.
    f(0)=0f(0) = 0 but f′(0)f'(0) not necessarily zero
  4. D.
    ∣f(x)∣≤1,x∈[0,1]|f(x)| \leq 1, x \in [0, 1]
Show answer

Correct option: B

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