Final answer:
The Rockefeller Foundation, Vanderbilt University, and the Carnegie Library are examples of the philanthropic efforts of wealthy industrialists like Rockefeller and Carnegie, who used their fortunes to support learning and societal welfare.
Step-by-step explanation:
The Rockefeller Foundation, Vanderbilt University, and the Carnegie Library exemplify the idea of philanthropy. These institutions were established as part of a larger movement in which wealthy industrialists, like John D. Rockefeller and Andrew Carnegie, believed that they had a social responsibility to use their wealth to support learning and enrich society. Carnegie, in particular, promoted this through his essay 'The Gospel of Wealth', wherein he argued that affluent individuals should use their fortunes to benefit the public good by funding institutions that advance education, science, and culture.
Rockefeller made substantial contributions to education, including a $500 million donation that helped establish the University of Chicago. Carnegie's philanthropy extended to constructing public libraries and supporting scientific research; notably, he left ninety percent of his fortune for philanthropic purposes after his death. Their efforts were seen as acts to mitigate the inequalities produced by their business practices and to provide a form of support to those less fortunate. This approach to wealth and the financing of public works became a hallmark of the period at the end of the nineteenth century, reflecting the ideals of the elite to give back to society.