AP Calculus FRQ Review: In-Out Rates

A classic AP Calculus Free Response Question: interpreting a situation with an "In" and an "Out" rate: adding something while also taking it away. How to use integrals and derivatives to calculate accumulated amount gained, lost, combined with an initial amount, when the amount was at an absolute maximum or minimum, and how to use the TI-84 graphing calculator to help do it all!