Life’s most persistent and urgent question is, “What are you doing for others?”

Martin Luther King, Jr. (1929–1968) American clergyman, civil rights leader, social activist, preacher

Sermon (1963 ed.), “The Three Dimensions of a Complete Life,” “2. Breadth”
    (Source)

Sermon on Revelation 21:16.

As with many of King's sermons and writings, this one exists in many forms given over the years. While there are indications that the sermon was first developed in early 1952, and a version being preached at Ebenezer Baptist Church (1953-09-06), the earliest documented version is was given as his audition as pastor at Dexter Avenue Baptist Church, Montgomery, Alabama (1954-01-24), under the title "The Dimensions of a Complete Life." That version, however, does not include this phrase or the surrounding text.

King collected a version of the text in his book The Measure of a Man, "The Dimensions of a Complete Life" (1959), as he continued to evolve and repeat the sermon (e.g., 1960, 1960), almost on a yearly basis.

The text of the sermon was fleshed out when collected in Strength to Love, ch. 9 (1963); and that is where this particular phrase can be found; that is what is cited above.

While this text is missing in most versions of this sermon, in some later ones (e.g., New Covenant Baptist Church, Chicago, 1967-04-09), King invokes the Parable of the Sheep and the Goats (Matthew 25:31–46), framing it as contemporary individuals facing Christ after death, ending with Christ asking, "What did you do for others?" and then adding the comment, "Somewhere along the way, we must learn that there is nothing greater than to do something for others."

For more discussion about this quotation, see Quote Origin: Life’s Most Persistent and Urgent Question Is, “What Are You Doing for Others?” – Quote Investigator®.