what is the maximum number of possible extreme values for the function, f(x)=x³ - 7x - 6?\na. 1\nb. 2\nc…

Explanation:

Step1: Recall the relationship between degree and extrema

The number of extreme - values of a polynomial function (y = f(x)) is at most one less than the degree of the polynomial.

Step2: Determine the degree of the given polynomial

The function (f(x)=x^{3}-7x - 6) is a polynomial of degree (n = 3) (since the highest - power of (x) is 3).

Step3: Calculate the maximum number of extreme values

Using the rule that the maximum number of extreme values of a polynomial is (n - 1), where (n) is the degree of the polynomial. For (n = 3), the maximum number of extreme values is (3-1=2).

Answer:

B. 2