Stage: 5 Challenge Level:
This could just be a straightforward calculus exercise except that
you are asked first to consider the geometric situation and make
conjectures about the result before you do any calculus.
To appreciate and fully understand the mathematics you are learning
it is good practice to make conjectures if you can and then review
your first thoughts in light of further work on the problem.
It is important to ask yourself how many answers you might expect
to find (one only or perhaps more than one?) and to ask yourself
how you will know if you have found ALL the answers.