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In mathematics, a real-valued function defined on an interval (or on any convex subset of some vector space) is called convex, concave upwards, concave up or convex cup, if for any two points x and y in its domain C and any t in [0, 1],In other words, a function is convex if and only if its epigraph (the set of points lying on or above the graph) is a convex set. Pictorially, a function is called 'convex' if the function lies below or on the straight line segment connecting two points, for any two points in the interval.