Question

Rogelio is asked to sketch a graph of g(x)=3x3(x−5)2(5−x)4
. How many turning points should his sketch include?(1 point)
Responses

nine at most
nine at most

three at most
three at most

eight at most
eight at most

exactly eight

Answer 1

eight at most

Reason: (5−x)^4 = (x−5)^4, so g(x)=3x^3(x−5)^6 is a degree 9 polynomial. A polynomial of degree n has at most n−1 turning points, so at most 8.