[[Convex function]]
# A twice-differentiable function is convex iff its second derivative is nonnegative everywhere

Let $f : (a,b) \to \mathbb{R}$ be a $C^2$ [[Differentiability|differentiable]] function.
Then $f$ is [[Convex function|convex]] iff $f''(x) \geq 0$ for all $x \in (a,b)$. #m/thm/anal
Furthermore if $f''(x) > 0$ for all $x \in (a,b)$, then $f$ is strictly convex.

> [!missing]- Proof
> #missing/proof

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