I seems that Maple doesn't know anything about the convexity of functions.
It would be nice to have a command to check the convexity of (real) functions in Maple, also Maple should have knowledge on the convexity of known functions: for example: constant function, linear function , abs, sin (convex on a specific region) etc.
To deal with the calculus of convex functions: for example Maple should know such theorems: if f(x) and g(x) are convex functions and g(x) is non-decreasing then g(f(x)) is convex, etc.
