question 17 of 25\nwhat is the maximum number of relative extrema contained in the graph of\nthis…

question 17 of 25\nwhat is the maximum number of relative extrema contained in the graph of\nthis function?\n$f(x)=3x^{3}-x^{2}+4x - 2$

question 17 of 25\nwhat is the maximum number of relative extrema contained in the graph of\nthis function?\n$f(x)=3x^{3}-x^{2}+4x - 2$

Answer

Explanation:

Step1: Recall the degree of the function

The given function (f(x)=3x^{3}-x^{2}+4x - 2) is a polynomial function. The degree (n) of a polynomial (y = a_{n}x^{n}+a_{n - 1}x^{n-1}+\cdots+a_{1}x + a_{0}) is (n = 3) (the highest power of (x)).

Step2: Use the relationship between degree and number of relative extrema

For a polynomial function (y=f(x)) of degree (n), the number of relative extrema (r) satisfies (r\leq n - 1).

Answer:

(2)