Convexity is a unique nature of function, it has geometric significance, and also algebra, concave or convex and convex (concave) function in inequality, functional analysis, optimization theory, mathematical programming, operations research, control, mathematical economics discussed and other areas of mathematics research in and application of which are widely used, research in this area has been a convex sets of forms with a specific direction, that is convex Background made it very easy to understand, only the study of images from the function can be made of the need to bump, but here are reflected in The Combination of mathematical thinking is very This paper introduces some basic concepts of the function Convexity, followed by the concave and convex functions are given to judge some of the conditions discussed here are also low-level geometric meaning of derivative, and finally introduced the concave and convex function of some simple application, a turning point in leads demonstrated under the definition of concave and convex role in the functional diagram, after the out of the Jensen inequality shows Convexity inequalities among the magical Key words :function; concave and convex; derivative; inflection point; Jensen inequality
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