Find the inflection points, if any, of the function. 
Definitions:
Death Penalty
A government-sanctioned practice where a person is executed by the state as a punishment for a crime, typically for serious offenses like murder.
Serial Killers
Individuals who commit a series of murders, typically three or more, over a period of time, often with cooling-off periods in between, driven by abnormal psychological gratification.
Homicide Rate
The number of homicides in a given area over a specific period of time, often reported per 100,000 people per year.
Sociological Theories
Frameworks for understanding how individuals interact within society and how structures influence behaviors.
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