\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
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Which conditions uniquely define the exponential function \(\exp\) on \(\mathbb{R}\)?
\(f' = f\) and \(f(0) = 1\)
\(f' = f\) and \(f(1) = 0\)
\(f' = 1\) and \(f(0) = 1\)
\(f' = f\) and \(f(0) = 0\)
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