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convex function

A function whose chord between any two points lies on or above the curve.

A function $g$ is convex on $[a,b]$ if $g(\lambda x_1 + (1-\lambda)x_2) \leq \lambda g(x_1) + (1-\lambda)g(x_2)$ for all $x_1,x_2\in[a,b]$ and $\lambda\in[0,1]$ .

Examples

$x^2$ and $e^x$ are convex everywhere.