Turning point

Definition

A turning point is a point on the graph of a polynomial function where the graph changes direction from increasing to decreasing or vice versa. It occurs at local maxima or minima.

5 Must Know Facts For Your Next Test

1. The number of turning points of a polynomial function is at most one less than its degree.
2. A polynomial of degree n can have up to n-1 turning points.
3. Turning points occur at critical points where the derivative equals zero or is undefined.
4. The nature of a turning point (local maximum or minimum) can be determined using the second derivative test.
5. Graphically, turning points are where the curve changes concavity.

Review Questions

• How do you determine the number of possible turning points for a given polynomial?
• What is the relationship between critical points and turning points?
• How can you use derivatives to identify and classify turning points?

Related terms

Critical Point: A point on the graph where the first derivative is zero or undefined, which could indicate a local maximum, minimum, or saddle point.

Local Maximum:

A point where the function value is higher than all other nearby values.

Local Minimum:

A point where the function value is lower than all other nearby values.