what is the maximum number of relative extrema contained in the graph of this function?\nf(x)=3x^3 - x^2 +…
what is the maximum number of relative extrema contained in the graph of this function?\nf(x)=3x^3 - x^2 + 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
The function (f(x)=3x^{3}-x^{2}+4x - 2) is a polynomial function. The highest - power of (x) is (n = 3).
Step3: Calculate the maximum number of relative extrema
Using the formula that the maximum number of relative extrema of a polynomial is (n - 1), substituting (n = 3) gives (3-1=2).
Answer:
2