Final answer:
The maximum number of turning points for the graph of a fifth degree polynomial is four, as the number of turning points for any polynomial is at most its degree minus one.
Step-by-step explanation:
The maximum number of turning points for the graph of a fifth degree polynomial is four.
A turning point is a point at which the direction of the graph changes, meaning the graph goes from increasing to decreasing, or vice versa.
The number of turning points of a polynomial of degree n is at most n - 1.
For a fifth degree polynomial, which is a polynomial of the form f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f where a, b, c, d, e, and f are constants and a is non-zero, the maximum number of turning points can be found by subtracting one from the degree of the polynomial, which is five.
Therefore, the maximum number of turning points is 5 - 1 = 4.