Turning Point

A turning point is a point where the graph of a function changes from increasing to decreasing or vice versa. In other words, the turning points correspond to the relative extrema of the graph of a function.

The graph corresponds to a fifth-degree polynomial with four turning points. When dealing with polynomial functions, there is a close connection between the degree, the zeros, and the turning points.

1. The graph of a polynomial function of degree n can have at most n - 1 turning points.
2. If a polynomial function has n distinct real zeros, then its graph has exactly n - 1 turning points.