Question

question 17 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 degree of the function

The given function \(f(x)=3x^{3}-x^{2}+4x - 2\) is a polynomial function. The degree \(n\) of a polynomial \(y = a_{n}x^{n}+a_{n - 1}x^{n-1}+\cdots+a_{1}x + a_{0}\) is \(n = 3\) (the highest power of \(x\)).

Step2: Use the relationship between degree and number of relative extrema

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

Answer:

\(2\)