A problem of vectors and functions, please help

well it seems that it was something simple xD, thanks
But since we are here, I would like to know that it takes into account the maximize function, although the first requirement argument is the function, the second argument is a value that remains to be defined by the user that will give me a local maximum of the evaluated function. In the case of evaluating M_k with a parameter between 0 and 10, it gives me a value of 3 that corresponds to the maximum value of the function between that range, but if I wanted the second value that corresponds to 4.
Now if I assign a value between 11 and 20 as a parameter, it should give me 21, which corresponds to the maximum value, however, sometimes it gives me 19.5, sometimes 19. Why is this? Although this is a problem of maximums and minimums in a function, I am not allowed to apply derivatives since the function is generated from conditionals.

Yes, that was my mistake, I was using a range with a unit assigned as the index of a vector, which is meaningless, I didn't understand how this type of vectorization worked. I already understood it, thank you very much. Now I only have the doubt of why the maximize function gave those results.