question 6 of 21 what is the maximum number of relative extrema contained in the graph of this function…
question 6 of 21 what is the maximum number of relative extrema contained in the graph of this function? f(x)=3x^4 - x^2 + 4x - 2 answer here
Answer
Explanation:
Step1: Recall the relationship between degree and extrema
The maximum number of relative extrema of a polynomial function $y = f(x)$ is one less than the degree of the polynomial.
Step2: Determine the degree of the given polynomial
The function $f(x)=3x^{4}-x^{2}+4x - 2$ is a polynomial of degree $n = 4$ (the highest - power of $x$ is 4).
Step3: Calculate the number of relative extrema
Using the formula $n-1$, where $n = 4$, we get $4 - 1=3$.
Answer:
3