If is continuous function in and

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

If f(x)f(x) is continuous function in [0,2π][0, 2\pi] and f(0)=f(2π)f(0) = f(2\pi), then prove that there exists a point c∈(0,π)c \in (0, \pi) such that f(c)=f(c+π)f(c) = f(c + \pi) .

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