Question

question 6 of 14
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 number of relative extrema of a polynomial function \(y = f(x)\) is at most \(n - 1\), where \(n\) is the degree of the polynomial.

Step2: Determine the degree of the given polynomial

For the function \(f(x)=3x^{5}-x^{3}+4x - 2\), the highest - power of \(x\) is \(n = 5\).

Step3: Calculate the maximum number of relative extrema

Using the formula \(n-1\), we substitute \(n = 5\) to get \(5 - 1=4\).

Answer:

4