Extremal points of a function.

- The function has an absolute maximum at if .
- The function has a relative (or local) maximum at if there exists an interval such that .
- The function has an absolute minimum at if .
- The function has a relative (or local) minimum at if there exists an interval such that .
- A maximum and a minimum are called extremal points (singular: extremum

- The absolute value function has an absolute maximum at 0, but has no minimum (see Figure 6(a)).
- The function such that has no extremum (see Figure 6(b)).
- The sine function has an absolute maximum at every point
and an absolute minimum at every point
(in both cases,
denotes an integer); see Figure 6(c).
- The function such that has a local maximum at and a local minimum at ; see Figure 7. In order to draw the graph, the reader has to first draw a table, as in Chapter 1, section section absolute value; as the function is ``affine by parts'', the drawing process is easy.

Noah Dana-Picard 2007-12-28