Question
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
Exactly eight
eight at most
nine at most
Three at most
Answers
GPT 3.5
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."
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."