Final answer:
During the Gilded Age, Captains of Industry like Andrew Carnegie and John D. Rockefeller typically participated in philanthropy by building libraries and funding education, following the belief that the wealthy owed a debt to society.
Step-by-step explanation:
A typical philanthropic activity during the Gilded Age by the Captains of Industry such as Andrew Carnegie and John D. Rockefeller was building libraries and funding education. These industrialists amassed huge fortunes and some, like Carnegie, believed they owed a debt to society due to their success. Carnegie, for instance, used his wealth to fund the construction of libraries, schools, and institutions of higher learning, and wrote about the responsibility of the wealthy to find proper uses for their wealth in his essay 'The Gospel of Wealth'. Rockefeller also engaged in philanthropy, establishing foundations that supported education and public health.