question 6 of 14\nwhat is the maximum number of relative extrema contained in the graph of this…
question 6 of 14\nwhat is the maximum number of relative extrema contained in the graph of this function?\nf(x)=3x^5 - x^3 + 4x - 2
Answer
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