Delving Deeper: Optimization on Discrete Domains Using Calculus

Whether teaching calculus or simply living life, we often find ourselves confronted with functions that we would like to optimize. For example, suppose that we have a function that tells us the amount in millions of dollars that we will earn as profit by producing x units of widgets. Suppose, for example, that our profit function is given by f ( x ) = -9 x 3 + 71 x 2 - 91 x