Turning point

Definition

A turning point of a polynomial function is where the graph changes direction from increasing to decreasing or vice versa. It is often associated with local maxima and minima.

5 Must Know Facts For Your Next Test

1. A polynomial of degree $n$ can have at most $n-1$ turning points.
2. Turning points occur at critical points where the derivative is zero or undefined.
3. Turning points help determine the overall shape and behavior of a polynomial graph.
4. The second derivative test can be used to identify whether a critical point is a turning point.
5. Local maxima and minima are specific types of turning points.

Review Questions

• What is the maximum number of turning points for a polynomial of degree 5?
• How do you determine if a critical point is a turning point?
• What role do turning points play in understanding the graph of a polynomial function?

Related terms

Critical Point: A point on the graph where the first derivative is zero or undefined.

Local Maximum: A point where the function value is higher than all nearby points.

Local Minimum: A point where the function value is lower than all nearby points.