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

guarantees .

c. Give an additional condition on *g* alone and show that it

guarantees .

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