StellarThe Candidates Test is used to find absolute maxima and minima of a continuous function on a closed interval. The idea is simple: the absolute extrema must occur at either a critical point in the interval or at one of the endpoints. So to apply the test, students find all critical points in the interval, evaluate the function at each critical point and at the endpoints, and then compare those values. The largest value is the absolute maximum, and the smallest value is the absolute minimum.
This test works especially well because of the Extreme Value Theorem. If a function is continuous on a closed interval, then absolute extrema are guaranteed to exist, and the Candidates Test tells us exactly where to look for them.