Calculus observes the rates of change in functions and uses that to make sense of the general trends of graphs. Through differentiation ("taking the derivative"), one can find the instantaneous rate of change of a function at a given x coordinate. Through integration, the process is reversed and rates of change can be used to understand the original function.
Differentiation and integration are also useful in understanding compound interest, maximizing profit and minimizing cost, and supply/demand models. In both versions of the course, the student will gain a broad vocabulary of operations that form the basis of calculus.