Final answer:
The function f(x) = -9x⁶ + 9x² + 3x - 52 is a polynomial of degree 6. It can have a maximum of 5 turning points. These are the points where the function changes direction.
Step-by-step explanation:
In mathematics, the function f(x) = -9x⁶ + 9x² + 3x - 52 represents a polynomial of degree 6. The maximum number of turning points in any polynomial function is given by the degree of the polynomial minus 1. Thus, the given function has a maximum of 6-1= 5 turning points. Don't confuse turning points with zeros or roots of a polynomial. Turning points are where the function changes direction, like the tops and bottoms of hills and valleys in a graph. The number of turning points can be less than or equal to degree-1; it is not always equal to degree-1.
Learn more about turning points