Question

question 4 of 20
what is the maximum number of relative extrema contained in the graph of
this function?
f(x)=3x⁴−x²+4x−2

Explanation:

Step1: Recall the rule for relative extrema

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

Step2: Determine the degree of the function

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

Step3: Calculate the maximum number of relative extrema

Using the rule \( n - 1 \), substitute \( n = 4 \): \( 4-1=3 \).

Answer:

3