Final answer:
Carnegie and Rockefeller shifted their focus from accumulating wealth to philanthropy after J.P. Morgan's death, giving away large portions of their fortunes in various charitable endeavors.
Step-by-step explanation:
After the death of J.P. Morgan at the age of 75, Andrew Carnegie and John D. Rockefeller changed their competition approaches. Instead of trying to be the richest, they shifted their focus to philanthropy and began giving away their fortunes. This is reflected in Carnegie's publication of The Gospel of Wealth, where he expressed that the wealthy have an obligation to care for the less fortunate. Both Carnegie and Rockefeller are remembered not only for their industrial successes but also for their philanthropic contributions, such as funding libraries, universities, and various charitable causes.