Marginal Analysis

Let $R(x)$ be the revenue for a production $x$, $C(x)$ the cost, and $P(x)$ the profit. Then

$$P(x) = R(x)-C(x),$$

and the marginal profit for the $x_0$th unit is defined by

$$P'(x_0) = R'(x_0)-C'(x_0),$$

where $P'(x)$, $R'(x)$, and $C'(x)$ are the Derivatives of $P(x)$, $R(x)$, and $C(x)$, respectively.

See also Derivative