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If ƒ : R → R is a differentiable function such that f"(x) > 2f(x) for all x ∈ R, and f(0) = 1, then
  • a)
  • b)
    ƒ(x) is decreasing in (0,∞)
  • c)
     ƒ(x) is increasing in (0,∞)
  • d)
Correct answer is option 'A,C'. Can you explain this answer?
Verified Answer
If ƒ : R → R is a differentiable function such that f"(...
Given that,




∴ option (A) is correct

⇒ f(x) is strictly increasing on x ∈ (0, ∞)
⇒ option (C) is correct
As, we have proved above that

⇒ option (D) is incorrect
∴  options (A) and (C) are correct
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If ƒ : R → R is a differentiable function such that f"(x) > 2f(x) for all x ∈ R, and f(0) = 1, thena)b)ƒ(x) is decreasing in (0,∞)c)ƒ(x) is increasing in (0,∞)d)Correct answer is option 'A,C'. Can you explain this answer?
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