Rolle theorem states that for any real-valued differentiable function, that have equal values at any two distinct points is because of a stationary point lies between them. Stationary point is a point, where the first derivative is zero. Standard version of the theorem can be given as "If f(x) is continuous an [a,b] and differentiable on (a,b) and if f(a) = f(b) then there is some c in the interval (a,b) such that f '(c) = 0."
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