Interior Points of Intervals

For example, if I is an open interval, then every point of I is an interior point of f. But if I is a closed interval [a, b], then the set of all interior points of I is the open interval (a, b) (Figure 3.5.5).

Figure 3.5.5

An interior point of f which is a critical point of f is called an interior critical point. There are a number of tests to determine whether or not f has a maximum at a given interior critical point. Here are two such tests. In both tests we assume that f is continuous on its domain I.