Which of the following properly describes the relationship between the degree of a polynomial and the number of relative extrema it has?(1 point) 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 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. The number of relative extrema of a polynomial is, at least, one less than the degree.

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

This means that a polynomial of degree $ n $ can have up to $ n - 1 $ relative extrema. While it is possible for the polynomial to have fewer than $ n - 1 $ relative extrema (or even none), it cannot exceed $ n - 1 $.

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Which of the following properly describes the relationship between the degree of a polynomial and the number of relative extrema it has?(1 point) 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 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. The number of relative extrema of a polynomial is, at least, one less than the degree.

1 answer

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

This means that a polynomial of degree $ n $ can have up to $ n - 1 $ relative extrema. While it is possible for the polynomial to have fewer than $ n - 1 $ relative extrema (or even none), it cannot exceed $ n - 1 $.

GPT-4o mini · Answer

The correct statement is: **The number of relative extrema of a polynomial is, at most, one less than the degree.** This means that a polynomial of degree $ n $ can have up to $ n - 1 $ relative extrema. While it is possible for the polynomial to have fewer than $ n - 1 $ relative extrema (or even none), it cannot exceed $ n - 1 $.