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, 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 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 least, one less than the degree.
The number of relative extrema of a polynomial is, at most, one less than the degree.
The correct response is: The number of relative extrema of a polynomial is, at most, one less than the degree.
The correct answer is: The number of relative extrema of a polynomial is, at most, one less than the degree.
To explain how to arrive at this answer, we need to understand the relationship between the degree of a polynomial and the number of its relative extrema.
The degree of a polynomial refers to the highest power of the variable in the polynomial. For example, a polynomial of degree 3 would have the highest power of x as x^3.
The number of relative extrema of a polynomial is determined by the behavior of the polynomial at different points. The relative extrema occur at the points where the polynomial changes direction, such as local maxima or minima.
By analyzing the highest power of the polynomial, we can determine the maximum number of possible relative extrema. A polynomial of degree n can have at most n-1 relative extrema.
Hence, the correct answer is that the number of relative extrema of a polynomial is, at most, one less than the degree.