Some definitions of convex function and concave function in domestic and abroad are opposite convex function and concave function_ convex functions

Convex Function

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 was convex on a interval if to any two points and where,

(Rudin 1976, p. Cf. Gradshteyn and Ryzhik, p. 1132).

If has a second derivative in, then a necessary and sufficient as it to being condition on this convex is that th e second derivative for all in.

If The inequality above is strict to and, then is called Strictly.

Examples of convex functions include for or even, for, and to all. If The sign of the inequality is reversed, the function is called concave. Also:convex, concave function, Interval, logarithmically convex function REFERENCES:

Eggleton, R. B. and Guy, R. K. "Catalan strikes again! How likely are a Function to Yes convex? Math. Mag. 61, 211-219, 1988.

Gradshteyn, I. S and Ryzhik, M. Tables of Integrals, Series, and Products, 6th ed. San Diego, Ca:academic Press, p. 1 132, 2000.

Rudin, W. Principles of Mathematical Analysis, 3rd ed. New York:mcgraw-hill, 1976.

Webster, R. convexity. Oxford, England:oxford University Press, 1995.

Referenced on wolfram| Alpha:convex Function

Concave Function

A function is said to being concave on ' an interval if, as any points and in, the ' function is ' convex on ' that interval ( Gradshteyn and Ryzhik 2000). Also:convex Function REFERENCES:

Gradshteyn, I. S and Ryzhik, M. Tables of Integrals, Series, and Products, 6th ed. San Diego, Ca:academic Press, p. 1 132, 2000. Referenced on wolfram| Alpha:concave Function

From:http://mathworld.wolfram.com/convexfunction.html

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