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1. Convex Definition & Meaning - Merriam-Webster
Link: https://www.merriam-webster.com/dictionary/convex
Description: WEB1. a. : curved or rounded outward like the exterior of a sphere or circle. b. : being a continuous function or part of a continuous function with the property that a line joining any two points on its graph lies on or above the graph. 2. a. of a set of points : containing all points in a line joining any two constituent points. b.
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2. Convex function - Wikipedia
Link: https://en.wikipedia.org/wiki/Convex_function
Description: WEBIn mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set.
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3. Convex Polygon - Definition, Formulas, Properties, Examples
Link: https://www.cuemath.com/geometry/convex/
Description: WEBA convex polygon is a shape in which all of its sides are pointing or protruding outwards. No two line segments that form the sides of the polygon point inwards. Also, the interior angles of a convex polygon are always less than 180°. Convex is used to describe a curved or a bulged outer surface.
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4. Convex Polygon – Definition, Formula, Properties, Types, Examples
Link: https://www.splashlearn.com/math-vocabulary/convex-polygon
Description: WEBConvex polygon is defined as a closed figure having all the interior angles less than 180 ∘. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. No sides are pointing inward. A triangle is …
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5. Convex Definition (Illustrated Mathematics Dictionary) - Math is Fun
Link: https://www.mathsisfun.com/definitions/convex.html
Description: WEBDefinition of. Convex. more ... Curved outwards. Example: A polygon (which has straight sides) is convex when there are NO "dents" or indentations in it (no internal angle is greater than 180°) The opposite idea is called "concave". See: Concave. Illustrated definition of Convex: Curved outwards.
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6. CONVEX Definition & Usage Examples | Dictionary.com
Link: https://www.dictionary.com/browse/convex
Description: WEBOct 10, 2013 · Compare concave (def. 1). Mathematics. (of a polygon) having all interior angles less than or equal to 180°. (of a set) having the property that for each pair of …
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7. 4.6: CONVEX FUNCTIONS AND DERIVATIVES - Mathematics …
Link: https://math.libretexts.org/Bookshelves/Analysis/Introduction_to_Mathematical_Analysis_I_(Lafferriere_Lafferriere_and_Nguyen)/04%3A_Differentiation/4.06%3A_Section_6-
Description: WEBLet \(I\) be an open interval and let \(f: I \rightarrow \mathbb{R}\) be a differentiable function. Then \(f\) is convex if and only if \(f^{\prime}\) is increasing on \(I\). Proof. Suppose \(f\) is convex. Fix \(a < b\) with \(a, b \in I\). By Lemma 4.6.5, for any \(x \in (a, b)\), we have \[\frac{f(x)-f(a)}{x-a} \leq \frac{f(b)-f(a)}{b-a} .\]
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8. CONVEX | definition in the Cambridge English Dictionary
Link: https://dictionary.cambridge.org/us/dictionary/english/convex
Description: WEBCONVEX | definition in the Cambridge English Dictionary. Meaning of convex in English. convex. adjective. us / ˈkɑːn.veks / / kənˈveks / uk / ˈkɒn.veks / / kənˈveks / Add to word …
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9. Convex Function -- from Wolfram MathWorld
Link: https://mathworld.wolfram.com/ConvexFunction.html
Description: WEBMar 15, 2024 · A convex function is a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the interval . More generally, a function is convex on an interval if for any two points and in and any where , (Rudin 1976, p. 101; cf. Gradshteyn and Ryzhik 2000, p. 1132).
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10. CONVEX | English meaning - Cambridge Dictionary
Link: https://dictionary.cambridge.org/dictionary/english/convex
Description: WEBCONVEX | English meaning - Cambridge Dictionary. Meaning of convex in English. convex. adjective. uk / ˈkɒn.veks / / kənˈveks / us / ˈkɑːn.veks / / kənˈveks / Add to word …