question 19 of 25\nwhat is the maximum number of relative extrema contained in the graph of this…
question 19 of 25\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 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