# 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

https://brainmass.com/math/computing-values-of-functions/continuous-functions-closed-intervals-32645

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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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