If you had a function on integers, f(n)= profit made by selling n items, then the "marginal profit" would be the profit from sellingone more: f(n+1)- f(n)= [f(n+1)- f(n)]/1. In the continuous case, f(x)= profit from selling x "gallons" (so it makes sense to have fractional x), the marginal profit is, as you say, the derivative, lim [f(x+h)- f(x)]/h. And the derivative is, of course, the slope of the tangent line to the graph.