Filling a Container Defined by a Curve

Teaching suggestions: As a precalculus exercise, before moving the slider to the right, try to sketch for a particular container shape. First try this with simple containers whose profiles are linear segments and then try curved profiles. For a calculus exercise, indicate on the sketch where the curves are concave up, concave down, or neither. Where are the inflection point(s), if any? What is the relationship between and ? Students might find it easier to sketch if they think of pouring a liquid into the container at a constant rate and then considering .