A researcher wants to study the relationship between the type of sport and the type of injury in studentathletes from a certain
high school. Of the 345 student athletes in the school who have had injuries, 100agreed to participate in the study and will give the researcher legal permission to view their records of sportsinjuries. From the records, the researcher will record the sport and the type of injury.
has a horizontal tangent line at , and it's clear from the plot that is increasing to the left and descreasing to the right. This means when , so there is an inflection point there and only statement II is true.
Statement III is not true because critical points only occur where or (possibly) when is undefined. Clearly when .