Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Discrete mathematics, continuous mathematics, and probability / Continuous mathematics / 4 / a / i

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- Solution i

Solution

The second-derivative criterion for convexity is

f is convex on R ⟺ f^{''} (x) \geq 0 for every x \in R .

The non-strict inequality is necessary and sufficient; the stronger condition

f^{''} > 0

is sufficient for strict convexity.

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