# 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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