Given that the polynomial f(x) has degree 4, which of the following most accurately describes the number of turning points of f(x)?
Select the correct answer below:
a. The graph of f(a) has at least 5 turning points.
b. The graph of f(x) has at least 4 turning points.
c. The graph of f(a) has at most 5 turning points.
d. The graph of f(x) has at most 3 turning points.
e. The graph of f(x) has at most 4 turning points.
f. The graph of f(a) has at least 3 turning points

The rule for polynomials is that for a polynomial degree n, the graph will have, at most, n - 1 turning points. For us, if we have a 4th degree polynomial, we will have, at most, 3 turning points. D is your answer.

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MrRoyal MrRoyal · Answer 2 · 2021-09-09T07:49:44+02:00

The turning point of a polynomial is a function of the degree of the polynomial. The true statement about the 4th degree polynomial is:

The graph of f(x) has at most 3 turning points.

Given that:

[tex]n = 4[/tex] ---- the degree of the polynomial

The maximum number of turning point (tp) in a polynomial is calculated as follows:

[tex]tp =n - 1[/tex]

Substitute [tex]n = 4[/tex]

[tex]tp =4 - 1[/tex]

[tex]tp =3[/tex]

This means that the turning point of the 4th degree polynomial is at most 3.

Hence, the correct option is (d)