Question

5.6.3 quiz: graphing polynomial functions
question 2 of 10
what is the maximum number of possible extreme values for the function,
$f(x)=x^{3}-7x - 6$?
a. 2
b. 4
c. 3
d. 1

Explanation:

Step1: Recall the formula for the maximum number of extreme values

For a polynomial function \(y = f(x)\) of degree \(n\), the maximum number of extreme values is \(n - 1\).

Step2: Determine the degree of the given polynomial

The given function is \(f(x)=x^{3}-7x - 6\). The highest power of \(x\) is \(3\), so the degree \(n = 3\).

Step3: Calculate the maximum number of extreme values

Using the formula \(n-1\), substitute \(n = 3\). Then \(n - 1=3 - 1=2\).

Answer:

A. 2