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Find a function that is defined in [0,1], but only continuous and differentiable on (0,1). The mean value theorem doesn't work, so that there is

Find a function that is defined in [0,1], but only continuous and differentiable on (0,1). The mean value theorem doesn't work, so that there is no c(0,1) so that f(c) =f(1)f(0)

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