Not a standard inequality

Calculus Level 5

Consider all differentiable functions \(f(x): \mathbb{R} \rightarrow \mathbb{R}\) that satisfy

  • \(f(x)\) is always positive,
  • \(f(x)+f'(x)\) is always positive.

Find the supremum of possible values of \(\dfrac{f(0)}{f(1)}\).


Harder version

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