Complete Convex Function
A function f(x) is completely convex in an open interval (a, b) if it has derivatives of all orders there and if (-1)^k f^(2k)(x)>=0 for k = 0, 1, 2, ... in that interval. For example, the functions sin x and cos x are completely convex in the intervals (0, π) and (-π/2, π/2) respectively.