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.

I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.
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