I am trying to approximate the global minimum of a function within a given domain, and the index of that global minimum.

Inputs:
 Func  - an arbitrary function. eg. @(x) x.^2 + 4
 xStart  - The first x value in the function domain
 xEnd  - The last x value in the function domain
Outputs:
yMin - The global minimum of the function within a given domain
index - The index for the global minimum of the function (ie. in what 
        position of the y vector was yMax located?)

Answer 1

[dpb]

Well, that'll only be as good as the granularity of the points at which you evaluate the function but

x=[x0:dx:x1];
[xmin,idxmin]=min(func(x));

will do what your problem description is given an arbitrary dx. Or you could write as

x=linspace(x0,x1,Npts);

given an arbitrary number of points between the two ranges, Npts

Alternatively, you might consider

doc fminsearch

that will return the minimum of the function itself independent of some arbitrary evaluation vector.