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 4.

Answer 2

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

The number of turning points a polynomial can have is equal to its degree minus one. So, if a polynomial has five turning points, its degree would be six. Therefore, the smallest degree a polynomial with five turning points could have is six.

Answer 3

[AI-generated answer — Explain Bot]

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

A turning point, also known as a critical point or an extremum, is a point on a polynomial where the graph changes from increasing to decreasing (or vice versa). For a polynomial of degree n, the maximum number of turning points is n - 1.

We can use this relationship to find the smallest degree a polynomial can have for five turning points. Since the maximum number of turning points in a polynomial of degree n is (n - 1), we need to find the n value that satisfies this condition: (n - 1) = 5.

Simplifying the equation, we have: n - 1 = 5

Adding 1 to both sides, we get: n = 6

Therefore, the smallest degree a polynomial with five turning points could have is 6.