Extreme Values of a Polynomial

The graph of a polynomial of degree n has at most n – 1 extreme values (minima and/or maxima). The total number of extreme values could be n – 1 or n – 3 or n – 5 etc.

For example, a degree 9 polynomial could have 8, 6, 4, 2, or 0 extreme values. A degree 2 (quadratic) polynomial must have 1 extreme value.