ASSIGNMENT 2·11 for SECTION 001
There are two parts to this assignment. The first part is online at www.mathxl.com. The second part consists
of the questions on this page. Your solutions must be typeset, preferably using LATEX. You are expected to
provide complete arguments and full justifications. Your paper must be stapled, with your name and student
number at the top of each page.
In the first century text Catoptrica, the ancient Greek mathematician Heron of Alexandria posed the following
problem:
Consider two points A and B on one side of a line. Find the point C on the line such that the combined
distance from A to C to B is minimal.
(Most of Heron’s texts were transmitted through their Arabic translations; this is the exact problem in
modern notation.) In this assignment, you will solve Heron’s problem.
1. Provide a labelled sketch of the problem.
2. Describe one nontrivial “real-life” situation where this problem might arise.
3. Solve the problem using differential calculus. Pay particular attention to the domain of the function you
establish.
4. Explain why differential calculus is not needed to solve the problem. (This is a bonus question.)