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  "body": "\n## Definition\n\nLet $I$ be an interval and let $f \\colon I \\to \\mathbb{R}$ be a function.\nThe function $f$ is convex if\n$$f(t x + (1 - t) y) \\le t f(x) + (1 - t) f(y)$$\nfor all $x, y \\in I$ and all $t \\in [0, 1]$.\n\n## Remarks\n\nGeometrically, each chord of the graph lies on or above the graph.\nFor example, $x^2$, $|x|$, and $e^x$ are convex on $\\mathbb{R}$. Linear functions are convex.\nA twice differentiable function with [[$f'' \\ge 0$ is convex|0Z41C17TGP]].\nMathlib defines convexity on a set as `ConvexOn`.\n\n## Explanations\n\n### L1 human\n\nA convex function bends upward, like a bowl.\nThe straight segment between two points of the graph never goes below the graph.\n",
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