Physical chemistry students often lack conceptual understanding of the measurable quantities derivatives and integrals represent in particular problems. Also, two-parameter equations of state exhibit horizontal inflections at the critical point in the "PV" isotherms, and students must employ the mathematical properties of inflections to obtain critical constants. Procedures for doing this can be memorized, but conceptual understanding is often lacking. A series of exercises is presented with the goal of exploring principles underlying the procedures that students routinely carry out. Although the bulk of the tutorials refer directly to calculus, an additional problem uses dimensional analysis, which provides a noncalculus method of obtaining critical constants. These exercises are intended to prepare students for the more complex problems they will face later in the term.