Imagine you’re designing a can to hold a fixed volume of soup but want to use as little metal as possible. Or you’re watching a balloon inflate and want to know how fast its radius grows when the volume increases at a certain rate. Or you’re stuck with a limit that gives 0/0. Calculus gives you tools for all these: optimization, related rates, and L’Hospital’s rule. This chapter connects derivatives to real‑world problem‑solving in three powerful ways.