determine the maximum number of turning points of f.\nf(x)=7x^6 - 6x^5 - 6x - 25\na) 7\nb) 6\nc) 5\nd) 0

Explanation:

Step1: Recall the formula for the maximum number of turning points

The maximum number of turning points of a polynomial function (y = f(x)) of degree (n) is (n - 1).

Step2: Find the degree of the polynomial (f(x)=7x^{6}-6x^{5}-6x - 25)

The degree (n) of the polynomial (f(x)=7x^{6}-6x^{5}-6x - 25) is the highest power of (x). Here, (n = 6).

Step3: Calculate the maximum number of turning points

Using the formula (n-1), substitute (n = 6). So the maximum number of turning points is (6 - 1=5).

Answer:

C. 5