The inherent authority of state and local governments to regulate individuals and private business in the name of public health promotion and protections is/are known as:

Police powers

Explanation:

As per the Constitution of the United States of America, police power is the state's capacity to control conduct and maintain order within its jurisdiction to improve the health, protection, morality and general welfare of its inhabitants. Police power comes under the jurisdiction of the legislative and executive branches, which they carry buy adoption and enforcement of laws.