There exists a function f ( x ) satisfying f (0) = 1, f ′(0) = –1, f ( x ) > 0 for all x…

Mathematics · JEE Advanced · NTA ExamsLimit, Continuity and Differentiability

There exists a function f (x) satisfying f (0) = 1, f ′(0) = –1, f (x) > 0 for all x and
  1. f ′ (x) > 0 for all x
  2. –1 < f ′(x) < 0 for all x
  3. –2 f ′(x) ≤ –1 for all x
  4. f ′(x) < –2 for all x

Answer

(D) f ′ ′ ( x ) x

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