Rolle's theorem
Theorem in real analysis
Rolle's theorem
In calculus and real analysis, Rolle's theorem (or lemma) states that a real-valued differentiable function which attains equal values at two distinct points must have a stationary point somewhere between them, that is, a point where its derivative is zero. The theorem is named after Michel Rolle. The theorem is a special case of, and is used to prove, the mean value theorem.
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