Question

determine the maximum number of turning points of f.
f(x)=7x^6 - 6x^5 - 6x - 25
a) 7
b) 6
c) 5
d) 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