Was that drawing part of the problem given?
Coffee is being poured into the mug shown in the figure at constant rate (measured in volume per unit time). Sketch a rough graph of the depth of the coffee in the mug as a function of time. Account for the shape of the graph in terms on concavity? What is the significance of the inflection point?
This does not make sense at all.
Ok. What I think your rough sketch should look like is the f(x)=x^(1/3) graph.
Ofcourse it must be shifted to the right and up so it begins at (0,0).
label the x-axis "time' and the y-axis "depth". So if you see the graph at the middle the inflection point represents the depth of the mug increasing as the thin part fills up.