Answer
If f is a polynomial function of degree n, then the graph of f has at most $n-1$ turning points.
Work Step by Step
We know that a turning point in the graph is the point where the function changes its direction. There are two cases as follows:
(1) If the function is increasing until this point, then the function would start decreasing after this point.
(2) If the function is decreasing until this point, then the function would start increasing after this point.
Thus, it can be concluded that a polynomial with the highest power of the variable as n would have at most $n-1$ turning points in its graph.
