The minima and maxima of a function can only occur at:
- Critical points of the function; or
- The boundaries that the function is being evaluated at
Critical points of the function are the places where the derivative equal 0.
So... take the derivative of the function and solve for 0. The resulting x are the critical points. For each critical point that is within the boundaries, evaluate the function at those locations. Also evaluate the function at the boundaries. Now the minimum out of all those evaluations is the global minima over that range, and the maximum out of those evaluations is the global maximum over that range.