So I will be giving a seminar to a scientifically mature lay audience (think bio/social science undergrad level). I have been told that I should count on less than half the audience to have experience with calculus. I think I can explain the basic optimization of $f(x)$ pictorially and introducing (and for some re-introducing) the concept of a derivative. Then I plan to go on to Lagrange multipliers and discrete time optimal control. I don't want to lose them though, so I want to know if anyone has any good explanations, analogies, videos, graphics (or anything else) that will keep a lay audience engaged. Note I will use Lagrange multipliers in the talk to explain a particular application, but I want to convey the message that the math is interesting in and of itself and that it can be used for a variety of things. I'm less concerned about the details being correct than getting the main message across. This portion of the seminar should be less than 15 minutes so I don't have that much time.