Determine the maximum number of turning points for the given polynomial function. $f\(\left\)(x\(\right\))=6x^4+2x$

• A. 1
• B. 2
• C. 3
• D. 4

Answer: (C)

Verified step by step guidance

1. Understand that the maximum number of turning points of a polynomial function is determined by its degree. The degree of a polynomial is the highest power of the variable x.
2. Identify the degree of the given polynomial function f(x) = 6x^4 + 2x. The term with the highest power of x is 6x^4, so the degree of the polynomial is 4.
3. Recall that the maximum number of turning points of a polynomial function is one less than its degree. Therefore, for a polynomial of degree n, the maximum number of turning points is n - 1.
4. Apply this rule to the polynomial f(x) = 6x^4 + 2x. Since the degree is 4, the maximum number of turning points is 4 - 1.
5. Conclude that the maximum number of turning points for the polynomial function f(x) = 6x^4 + 2x is 3.