Graphical Behavior
Maximum & Minimum
Example 2
Let P(x) = -x6 - 3x3 + x + 1.
There are two maximum points at (-1.11, 2.12) and (0.33, 1.22). There is a minimum at (-0.34, 0.78). The maximum value of 2.12 at x = -1.11 is the absolute maximum since no point on the graph is higher. The maximum value of 1.22 at x = 0. 33 is called a relative maximum, being the largest value "relative" to points close to it on the graph. The minimum value of 0 .78 at x = -0.34 is a relative minimum, being the smallest value "relative" to points close to it on the graph.