Question

question 19 of 25
what is the maximum number of relative extrema contained in the graph of this function?
f(x)=3x^5 - x^3 + 4x - 2

Explanation:

Step1: Recall the relationship between degree and extrema

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

Step2: Identify the degree of the polynomial

The given function \(f(x)=3x^{5}-x^{3}+4x - 2\) is a polynomial. The highest - power of \(x\) is \(n = 5\).

Step3: Calculate the number of relative extrema

Using the formula \(n - 1\), we substitute \(n = 5\). So the maximum number of relative extrema is \(5-1=4\).

Answer:

4