Which of the following properly describes the relationship between the degree of a polynomial and the number of relative extrema it has?(1 point)

Question

Responses

The number of relative extrema of a polynomial is equal to the degree.
The number of relative extrema of a polynomial is equal to the degree.

The number of relative extrema of a polynomial is, at least, one less than the degree.
The number of relative extrema of a polynomial is, at least, one less than the degree.

The number of relative extrema of a polynomial is always one less than the degree.
The number of relative extrema of a polynomial is always one less than the degree.

The number of relative extrema of a polynomial is, at most, one less than the degree.

Answer 1

The correct response is:

The number of relative extrema of a polynomial is, at most, one less than the degree.

This is based on the fact that a polynomial of degree \( n \) can have at most \( n-1 \) turning points (which correspond to relative extrema).