Question

A friend runs up to you and excitedly explains that she has found that she has found a function g with the following properties:

Answer 1

Given the start point of (0,1) and (1,5), the average slope is (5-1)/(1-0) = 4.  So the finding that g'(x) for the interval is <=3 cannot be true.  It might be for a small segment but not the entire interval.