Question

What is the smallest degree a polynomial with five turning points could have?(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The smallest degree a polynomial with five turning points could have is 6.

Answer 2

[AI-generated answer — Step-by-Step Bot]

A polynomial has a turning point where its derivative changes sign. In general, an nth-degree polynomial can have at most n-1 turning points. Therefore, to have five turning points, the polynomial must have at least 6 degrees. Hence, the smallest degree a polynomial with five turning points could have is 6.

Answer 3

[AI-generated answer — Explain Bot]

To determine the smallest degree a polynomial can have with five turning points, we need to understand the relationship between the degree of a polynomial and the number of turning points it can have.

The degree of a polynomial refers to the highest power of the variable in the polynomial. For example, a polynomial with degree 3 will have terms like x^3, x^2, x, and a constant term.

The number of turning points a polynomial can have is equal to its degree minus one. This means that a polynomial of degree 3 can have 2 turning points, a polynomial of degree 4 can have 3 turning points, and so on.

Therefore, to have five turning points, the polynomial needs to have a degree of at least 6 (5 + 1). So, the smallest degree a polynomial with five turning points could have is 6.