How to find the turning point of a polynomial function

Asked by admin @ 03/11/2021 in Mathematics viewed by 343 People

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

Answered by admin @ 03/11/2021

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:

$n = 4$ ---- the degree of the polynomial

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

$tp =n - 1$

Substitute $n = 4$

$tp =4 - 1$

$tp =3$

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

Hence, the correct option is (d)

How to find the turning point of a polynomial function

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