Question

question 5 of 25
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 relationship between degree of polynomial and number of relative extrema

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

Step2: Identify the degree of the given polynomial

The given function \(f(x)=3x^{3}-x^{2}+4x - 2\) is a polynomial. The highest - power of \(x\) is \(n = 3\) (since the term with the highest exponent is \(3x^{3}\)).

Step3: Calculate the maximum number of relative extrema

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

Answer:

\(2\)