Question
We can use the degree of a polynomial to determine the number of turning points it can have. The number of turning points can be up to one or more than the degree, and since relative extrema occur at turning points, the same can be said for the number of relative extrema.
1)true
2)false
1)true
2)false
Answers
GPT-4o mini
1) **True**
The statement correctly explains that the number of turning points of a polynomial can be at most one less than the degree of the polynomial. Therefore, the number of relative extrema (which occur at turning points) can also be determined similarly. A polynomial of degree \( n \) can have up to \( n-1 \) turning points (and, consequently, up to \( n-1 \) relative extrema). Thus, the statement is true.
The statement correctly explains that the number of turning points of a polynomial can be at most one less than the degree of the polynomial. Therefore, the number of relative extrema (which occur at turning points) can also be determined similarly. A polynomial of degree \( n \) can have up to \( n-1 \) turning points (and, consequently, up to \( n-1 \) relative extrema). Thus, the statement is true.