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 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:

---- the degree of the polynomial

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

Substitute

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

Hence, the correct option is (d)

Read more about polynomials at:

link

Step-by-step explanation:

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.

7

step-by-step explanation:

8

step-by-step explanation: