201k views
4 votes
In general, if fis a polynomial function of degree n, then the graph of f has at most ____ turning point

In general, if fis a polynomial function of degree n, then the graph of f has at most-example-1
User Gigi
by
5.4k points

1 Answer

2 votes

Answer: n-1

Step-by-step explanation:

Let's say we're dealing with a quadratic. The degree is n = 2. It has n-1 = 2-1 = 1 turning point, which is the vertex (either highest or lowest point depending how the parabola opens).

Now consider a cubic with degree n = 3. It has at most n-1 = 3-1 = 2 turning points. It could have less turning points, or none at all.

By definition, a turning point is when the curve goes from increasing to decreasing, or vice versa.

User Techlead
by
6.8k points