\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Use the mean value theorem to show that for every \(a, b \in \mathbb{R}\) with \(a < b\), there exists \(c \in ]a, b[\) with \(b^3 - a^3 = 3 c^2 (b - a)\).
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