Question

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

Reason: relative extrema occur at critical points where the derivative is zero. If the polynomial has degree n, its derivative has degree n−1, so it can have at most n−1 real zeros (hence at most n−1 relative extrema).