To determine the maximum or minimum of a function using Calculus I techniques, you first find its derivative to identify critical points where the derivative is zero or undefined. Then, by checking the sign of the derivative before and after these points, or using the second derivative test, you can determine if these critical points are local maxima, minima, or points of inflection. Absolute maximum and minimum values can be found by evaluating the function at critical points and endpoints in a closed interval.