In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.
In calculus, the Intermediate Value Theorem states that if is a continuous function on the closed interval and is any number between and , then there is at least one point so that $f(c) =y_0$.
When I first teach this, I’ll draw some kind of crude diagram on the board:
In this picture, is less than while is greater than . Hence the one-liner:
I call the Intermediate Value Theorem the Goldilocks principle. After all, is too low, and is too high, but there is some point in between that is just right.