There is no known mathematical way of doing that for arbitrary functions.
For a subset of functions, the general approach is to take the derivative of the function and solve for 0. Each point at which the derivative becomes 0 is a minimum, maximum, or saddle point; determining which case you have can be done by taking the second derivative and evaluating it at the location and checking whether the sign of that is positive or negative or 0.
Solving the derivative for 0 is not typically possible in closed form if the derivative is a polynomial of degree more than 4, and finding all of the zeros is not generally possible for the periodic functions such as the trig functions.
