\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that \(F = \{f \in C^1(\mathbb{R}, \mathbb{R}) : f(0) + f(1) = f'(0)\}\) is a subspace of \(C^1(\mathbb{R}, \mathbb{R})\).
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