# My Favorite One-Liners: Part 72

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 $f$ is a continuous function on the closed interval $[a,b]$ and $y_0$ is any number between $f(a)$ and $f(b)$, then there is at least one point $c \in [a,b]$ 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, $f(a)$ is less than $y_0$ while $f(b)$ is greater than $y_0$. Hence the one-liner:

I call the Intermediate Value Theorem the Goldilocks principle. After all, $f(a)$ is too low, and $f(b)$ is too high, but there is some point in between that is just right.

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