The main difference between static optimization and dynamic optimization is that, instead of dealing with a differential dx, which measures changes in the value of $y = f\left( x \right)$ , we must instead deal with a shift or variation of the curve $y\left( t \right)$ , which consists of many contributing pieces. For example, in solving Mr. Kuchenfresser’s various consumption problems in previous chapters, meeting the goal of maximizing his aggregate utility of consumption (a single value) required choosing an entire set of consumption values along a path. The optimization took place with respect to the entire set of consumption choices. We couldn’t choose one in isolation without understanding its impact on those who followed.