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Let $$f(x) = 2 + \cos x$$ for all real x.
STATEMENT-1: For each real t, there exists a point c in $$[t, t + \pi]$$ such that $$f'(c) = 0.$$
because
STATEMENT-2: $$f(t) = f(t + 2\pi)$$ for each real t.
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