Question
What is the maximum number of relative extrema that a sixth degree polynomial can have?(1 point)
Responses
four at most
four at most
six at most
six at most
three at most
three at most
five at most
Responses
four at most
four at most
six at most
six at most
three at most
three at most
five at most
Answers
GPT-4o mini
The maximum number of relative extrema a polynomial can have is determined by its degree. A sixth degree polynomial can have at most \( n - 1 \) relative extrema, where \( n \) is the degree of the polynomial.
For a sixth degree polynomial, the maximum number of relative extrema is:
\[
6 - 1 = 5
\]
Therefore, the correct response is:
**five at most.**
For a sixth degree polynomial, the maximum number of relative extrema is:
\[
6 - 1 = 5
\]
Therefore, the correct response is:
**five at most.**