Definition: A function of one variable is convex on an interval if the line segment between any two points of the graph of the function is above or on the graph of the function. .
Definition: If the line segment between any two points of the graph of a function is below or on the graph of the function, then the function is called concave.
From a graphical perspective a convex function follows (a part of) the shape of an upward opened parabola, while a concave function follows (a part of) the shape of a downward opened parabola.
Definition: If the line segment between any two points of the graph of a function is below or on the graph of the function, then the function is called concave.
From a graphical perspective a convex function follows (a part of) the shape of an upward opened parabola, while a concave function follows (a part of) the shape of a downward opened parabola.
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| concave function | convex function |