\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Apply the mean value theorem to \(f(x) = x^2\) on \([1, 3]\) and find an explicit \(c \in ]1, 3[\) such that \(f(3) - f(1) = f'(c) \cdot (3 - 1)\).
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