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JEE Main 1982 Mathematics question on Limits Continuity and Differentiability

There exists a function f(x)f(x) satisfying f(0)=1f(0)=1, f′(0)=−1f'(0)=-1, f(x)>0f(x)>0, ∀x\forall x and
  1. A.
    f′′(x)<0f''(x)<0, ∀x\forall x
  2. B.
    −1<f′′(x)<0-1<f''(x)<0, ∀x\forall x
  3. C.
    −2≤f′′(x)≤−1-2 \leq f''(x) \leq -1, ∀x\forall x
  4. D.
    f′′(x)<−2f''(x)<-2, ∀x\forall x
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Correct option: A

[1982]

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