Which of the following properly describes the relationship between the degree of a polynomial and the number of relative extrema it has?(1 point)ResponsesThe 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.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 relationship arises from the fact that the relative extrema occur at the critical points, where the derivative is equal to zero. A polynomial of degree \( n \) will have a derivative of degree \( n-1 \), which can have at most \( n-1 \) real roots. Therefore, the number of relative extrema (which corresponds to the number of critical points) can be at most \( n-1 \).