Calculus and Analysis > Calculus > Mean-Value Theorems >

Rolle's Theorem

Let f be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then if f(a)=f(b), then there is at least one point c in (a,b) where f^'(c)=0.

Note that in elementary texts, the additional (but superfluous) condition f(a)=f(b)=0 is sometimes added (e.g., Anton 1999, p. 260).

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