Question

what is the greatest number of turning points that ( f(x)=x^{5}+3x^{4}-5x^{3}-15x^{2}+4x + 12 ) could have? answer

Explanation:

Step1: Recall the rule for turning points

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

Step2: Identify the degree of the polynomial

The given polynomial \(f(x)=x^{5}+3x^{4}-5x^{3}-15x^{2}+4x + 12\) is of degree \(n = 5\).

Step3: Calculate the maximum number of turning points

Using the formula \(n-1\), substitute \(n = 5\). So, \(5-1=4\).

Answer:

\(4\)