Rogelio is asked to sketch a graph of g(x)=3x^3(x−5)^2(5−x)^4. How many turning points should his sketch include?
Exactly eight
eight at most
nine at most
Three at most
To determine the number of turning points in a graph, we need to count the number of times the graph changes from increasing to decreasing or from decreasing to increasing.
Since the given function, g(x) = 3x^3(x−5)^2(5−x)^4, is a polynomial function of degree 9, the graph can have at most 8 turning points.
Therefore, the correct answer is "eight at most."