A former colleague Bill Wardlaw (March 3, 1936-January 2, 2013) used to create a “Problem of the Week” for his US Naval Academy students, giving a prize of a cookie if they could solve it. One of them is given below.
Let a, b, and c be real numbers and let f and g be real valued functions of a real variable such that and .
a. Give an example in which .
b. Give an additional condition on f alone and show that it
c. Give an additional condition on g alone and show that it