Rather, I think he knew that the general shape of a -x^3 equation tells us that as x increases, y tends towards negative infinity. In fact, I don't think Sal didn't check the end behavior because he thought of it.
So the "bunch of consultants" who came with an equation for the costs couldn't have come up with an equation where the costs are always decreasing with an increase of the production, in the first place ^^Īnd while this law makes intuitive sense (ask to much of somebody or something and you'll kill the goose with the golden eggs), you don't need to take it for granted. It's an economic phenomenon called "Law of diminishing returns". Now, since we deal with a factory, there are reasons to believe that past a certain point, the more you add to the production, the less it will yield.
It is a good question, and you are mathematically right.
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