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Theorem: Intermediate Root Value Theorem

Let $[a,b]$ be a closed real interval and let $f:[a,b]\to\mathbb R$ be a continuous real function with $f(a) < 0$ and $f(b) > 0$ (or $f(a) > 0$ and $f(b) < 0$). Then there is a root value $x\in[a,b]$ with $f(x)=0$.

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References

Bibliography

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