Calculus: We state and prove Rolle's Theorem - if f(x) is continuous on [a, b], f is differentiable on (a, b), and f(a) = f(b), then there is an x in (a, b) with f'(x) = 0. The examples of (a) f(x) = x^2 -5x + 6 on [2, 3], and (b) f(x) = sin(x) on [pi/4, 3pi/4] are given.
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