◀ ▲ ▶Branches / Analysis / Theorem: Rolle's Theorem

Theorem: Rolle's Theorem

Let $a < b,$ $[a,b]$ be a closed real interval, and $f:[a,b]\to\mathbb R$ a continuous function with $f(a)=f(b)$. Further, let $f$ be differentiable on the open real interval $]a,b[.$ Then there is an $\xi\in ]a,b[$ with $f'(\xi)=0.$

In particular, between any two roots of $f$ there is a root of $f'$.

This theorem is named after Michel Rolle (1652 - 1719).

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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983