Although the short description of the Maximize() function mentions that it can find the maximum of a function within a range, its use is restricted to solve blocks (look up the full help info to find that).
In this case I would revert to highschool mathematics that says you can find extrema of a function there where the derivative of the function has zero's.
Now your function that you want to find the extrema of, M(x) is too awkardly defined (it's derivative is discontinuous at certain points) to subject to the differential operator:
But fortunately you have the derivative in the form of V(x). Ah, that one too is awkwardly defined, (because it is discontinuous at some points), and so:
But it's zero's are (known to be from the definition) as x=a and x=a+b.
So from the graph we discern that the maximum of M(x) occurs at x=a+b, and its value is M(a+b).
(note that this is the EXACT answer, the solution by Valery above is an approximation).
Problem solved.
Success!
Luc
