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    Continuous functions on closed intervals

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    Let f be a function that is continuous on the closed interval [0,1] and differentiable on the open interval (0,1). If f(0) = f(1), then which of the following statements must be true?
    A.
    f has a minimum at some x0 such that 0 < x0 < 1. B.
    f has a maximum at some x0 such that 0 < x0 < 1. C.
    f has a minimum at some x0 such that 0 < x0 < 1.
    D.
    f(x0) = 0 at every x0 such that 0 < x0 < 1. E.
    f(x0) = 0 at some x0 such that 0 < x0 < 1.
    solution

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    Let f be a function that is continuous on the closed interval [0,1] and differentiable on the open interval (0,1). If f(0) = f(1), then ...

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    The continuous functions on closed intervals are determined.

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