Given a task to accomplish, it is natural to ask what is the best way to achieve your goal? Maybe you are flying from Beijing to London and need the shortest flight path. Or you are selling fuel and you want to find a function P(t) that gives you the optimal price at time t to maximize your profit. Or you are crossing a river with a strong current and want to determine a propeller direction (as a function of time) so that you cross the river in the least amount of time. The number of possible questions like those above seems endless. During this lecture will discuss some of the above problems, a famous brain-teaser called the brachistochrone problem, and illustrate how to find solutions to these problems using a version of calculus that makes sense in infinite dimensions – the interesting field of variational calculus!