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Proposition: Convexity and Concaveness Test
Let $a < b,$ and let $f:(a,b)\to\mathbb R$ be a twice differentiable function on the open real interval $(a,b).$ Then $f$ is convex if and only if $f^{\prime\prime}(x)\ge 0$ for all $x\in]a,b[.$ Analogously, $f$ is concave, if and only if $f^{\prime\prime}(x)\le 0$ for all $x\in(a,b).$
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
