While the rules of differentiation allow us to compute the derivative of just about any function, there are practical situations in which these rules cannot be used. For example, in some applications, a relationship between two variables may be given as a set of data points, but not as a formula. In situations like this, the rate of change of one variable with respect to the other (that is, the derivative) might be needed, but the rules do not apply to sets of data. This project focuses on methods for approximating the derivative of a function at a particular point. Backward and Forward Difference Quotients Assuming the limit exists, the definition of the derivative 0 ( ) ( ) ( ) lim h f a h f a f ' a h implies that ( ) ( ) ( ) , f a h f a f ' a h (1) for h near 0. If h > 0, then (1) is referred to as a forward difference quotient and if h 0 and a backward difference quotient if h