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Let \(f : [0, 1] \to \mathbb{R}\) be continuous on \([0, 1]\), differentiable on \(]0, 1[\), with \(f(0) = f(1) = 0\). Show that there exists \(c \in ]0, 1[\) with \(f'(c) = 0\). (Direct application of Rolle.)
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