Question

5.10.2 test (cst): polynomial functions
question 22 of 22
what is the maximum number of relative extrema contained in the graph of this function?
$f(x)=3x^{3}-x^{2}+4x - 2$

Explanation:

Step1: Recall the formula for the maximum number of relative extrema

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

Step2: Determine the degree of the given polynomial function

The given function is \(f(x)=3x^{3}-x^{2}+4x - 2\). The highest - power of \(x\) is \(x^{3}\), so the degree \(n = 3\).

Step3: Calculate the maximum number of relative extrema

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

Answer:

\(2\)